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  • Cited by 112
Publisher:
Cambridge University Press
Online publication date:
May 2016
Print publication year:
2016
Online ISBN:
9780511902581

Book description

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.

Reviews

'There’s a lot in here but it is explained clearly with many outline algorithms and exercises … I’m sure it will become a standard reference in this area for some time because of the range of … techniques it describes and the care that has gone in to explaining them as clearly as possible given the technical nature of the subject.'

Keith A. Benedict Source: Contemporary Physics

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Contents


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References
Acton, F. S. 1970. Numerical Methods That Work. New York: Harper and Row.
Affleck, I., Kennedy, T., Lieb, E. L., and Tasaki, H. 1987. Rigorous results on valence bond ground states in antiferromagnets. Phys. Rev. Lett., 59, 799.
Affleck, I., Kennedy, T., Lieb, E. L., and Tasaki, H. 1988. Valence bond ground states in isotropic quantum antiferromagnets. Comm. Math. Phys., 115, 477.
Aho, A. V., Ullman, J. D., and Hopcroft, J. E. 1983. Data Structures and Algorithms. Lebanon, IN: Addison Wesley.
Aichhorn, M., Pourovskii, L., and Georges, A. 2011. Importance of electronic correlations for structural and magnetic properties of the iron pnictide superconductor LaFeAsO. Phys. Rev. B, 84, 054529.
Alet, F., Wessel, S., and Troyer, M. 2005. Generalized directed loop method for quantum Monte Carlo simulations. Phys. Rev. E, 71, 036706.
Allen, M. P., and Tildesley, D. J. 1987. Computer Simulations of Liquids. Oxford University Press.
Anderson, J. B. 1975. Random walk simulation of the SchrÖdinger equation: He+3.J. Chem. Phys., 63, 1499.
Anderson, J. B. 1976. Quantum chemistry by random walk. J. Chem. Phys., 65, 4121.
Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E., and Cornell, E. A. 1995. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 269, 198.
Anderson, P. W. 1973. Resonating valence bonds: a new kind of insulator?Mater. Res. Bull., 8, 153.
Anderson, P. W. 1987. The resonating valence bond state in La2CuO4 and superconductivity. Science, 235, 1196.
Andreev, A. F., and Lifshitz, I. M. 1969. Quantum theory of defects in crystals. Sov. Phys.JETP, 29, 1107.
Anisimov, V. I., and Gunnarsson, O. 1991. Density-functional calculation of effective Coulomb interactions in metals. Phys. Rev. B, 43, 7570.
Anisimov, V. I., Zaanen, J., and Andersen, O. K. 1991. Band theory and Mott insulators: Hubbard-U instead of Stoner-I. Phys. Rev. B, 44, 943.
Arnow, D. M., Kalos, M. H., Lee, M. A., and Schmidt, K. E. 1982. Green's function Monte Carlo for few fermion problems.J. Chem. Phys., 77, 5562.
Aryasetiawan, F., Imada, M., Georges, A., Kotliar, G., Biermann, S., and Lichtenstein, A. I. 2004. Frequency-dependent local interactions and low-energy effective models from electronic structure calculations. Phys. Rev. B, 70, 195104.
Assaad, F. F. 1998. SU(2) invariant auxiliary field quantum Monte Carlo algorithm for Hubbard models. In: Krause, E., and Jager, W. (eds.), High Performance Computing in Science and Engineering. New York: Springer-Verlag.
Assaad, F. F., and Lang, T. C. 2007. Diagrammatic determinantal quantum Monte Carlo methods: projective schemes and applications to the Hubbard-Holstein model. Phys. Rev. B, 76, 035116.
Barker, A. A. 1965. Monte Carlo calculations of the radial distribution functions for a proton-electron plasma. Aust. J. Phys., 18, 119.
Bartlett, J. H., Gibbons, J. J., and Dunn, C. G. 1935. The normal helium atom. Phys. Rev., 47, 679.
Batrouni, G., and Scalettar, R. T. 1990. Anomalous decouplings and the fermion sign problem. Phys. Rev. B, 42, 2282.
Baxter, R. J. 1982. Exactly Solved Models in Statistical Mechanics. London: Academic Press.
Baym, G., and Mermin, N. D. 1961. Determination of thermodynamic Green's functions. J. Math. Phys., 2, 236.
Beach, K. S. D., Alet, F., Mambrini, M., and Capponi, S. 2009. SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study. Phys. Rev. B, 80, 184401.
Bemmel, H. J. M., ten Haaf, D. F. B., van Saarlos, W., van Leeuwen, J. M. J., and An, G. 1994. Fixed-node quantum Monte Carlo method for lattice fermions. Phys. Rev. Lett., 72, 2442.
Berg, B. A., and Neuhaus, T. 1991. Multicanonical algorithms for first order phase transitions. Phys. Lett. B, 267, 249.
Berg, B. A., and Neuhaus, T. 1992. Multicanonical ensemble: a new approach to simulate first-order phase transitions. Phys. Rev. Lett., 68, 9.
Bethe, Hans A. 1935. Statistical theory of superlattices. Proc. Roy. Soc. London A, 150, 552.
Blaizot, J. P., and Ripka, G. 1986. Quantum Theory of Finite Systems. Cambridge, MA: MIT Press.
Blankenbecler, R., Scalapino, D. J., and Sugar, R. L. 1981. Monte Carlo calculations of coupled boson-fermion systems. I. Phys. Rev. D, 24, 2278.
BlÖte, H. W. J., and Nightingale, M. P. 1982. Critical behavior of the two-dimensional Potts model with a continuous number of states: a finite size scaling analysis. Physica A, 112, 405.
Blume, D., Lewerenz, M., Niyaz, P., and Whaley, K. B. 1997. Excited states by quantum Monte Carlo methods: imaginary time evolution with projection operators. Phys. Rev. E, 55, 3664.
Blume, D., Lewerenz, M., and Whaley, K. B. 1998. Excited states by quantum Monte Carlo method. Math. Comp. Simul., 47, 133.
Boehnke, L., Hafermann, H., Ferrero, M., Lechermann, F., and Parcollet, O. 2011. Orthogonal polynomial representation of imaginary-time Green's functions. Phys. Rev. B, 84, 075145.
Boguslawski, K., Marti, K. H., and Reiher, M. 2011. Construction of CASCI-type wavefunctions for very large matrices. J. Chem. Phys., 134, 224101.
Bonča, J., and Gubernatis, J. E. 1993a. Quantum Monte Carlo simulations of the degenerate single-impurity Anderson model. Phys. Rev. B, 47, 13137.
Bonča, J., and Gubernatis, J. E. 1993b. Real-time dynamics from imaginary-time quantum Monte Carlo simulations: tests on oscillator chains. Phys. Rev. B, 47, 13137.
Bonča, J., and Gubernatis, J. E. 1994. Degenerate Anderson impurity model in the presence of spin-orbit and crystal field splitting. Phys. Rev B, 50, 10427.
Boninsegni, M., and Prokof'ev, N. 2005. Supersolid phase of hard-core bosons on a triangular lattice. Phys. Rev. Lett., 95, 237204.
Booth, T. E. 2003a. Computing the higher k-eigenfunctions by Monte Carlo power iteration: a conjecture, corrigendum. Nucl. Sci. Eng., 144, 113.
Booth, T. E. 2003b. Computing the higher k-eigenfunctions by Monte Carlo power iteration: a conjecture. Nucl. Sci. Eng., 143, 291.
Booth, T. E. 2003c. Improvements to the Monte Carlo second eigenfunction estimation. Tech. rept. LA-UR-03-4100. Los Alamos National Laboratory.
Booth, T. E. 2009. Particle transport applications. Page 215 of: Rubino, G., and Tuffin, B. (eds.), Rare Event Simulation using Monte Carlo Methods. Chichester: Wiley.
Booth, T. E. 2010. Examples of superfast power iteration. Tech. rept. LA-UR-10-06663. Los Alamos National Laboratory.
Booth, T. E. 2011a. A multiple eigenvalue power iteration convergence metric. Tech. rept. LA-UR-11-02223. Los Alamos National Laboratory.
Booth, T. E. 2011b. A simple eigenfunction convergence acceleration method for Monte Carlo. In: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (MC2011).
Booth, T. E. 2011c. Test of the multiple k-eigenfunction convergence acceleration method in MCNP. Tech. rept. LA-UR-11-02222. Los Alamos National Laboratory.
Booth, T. E., and Gubernatis, J. E. 2009a. Monte Carlo determination of multiple extremal eigenpairs. Phys. Rev. E., 80, 46704.
Booth, T. E., and Gubernatis, J. E. 2009b. The sewing algorithm. Comp. Phys. Commun., 180, 509.
Bouchoud, J. P., Georges, A., and Lihuillier, C. 1988. Pair wave functions for strongly correlated fermions and the determinantal representation. J. de Phys., 49, 553.
Brissenden, R. J., and Garlick, A. R. 1986. Biases in the estimations of keff and its errors by Monte Carlo estimation. Annals of Nuclear Energy, 13, 63.
Brower, R., Chandrasekharan, S., and Wiese, U.-W. 1998. Green's functions from quantum cluster algorithms. Physica A., 261, 520.
Bryan, R. K. 1990. Maximum entropy analysis of oversampled data problems. Eur. Biophys. J., 18, 165.
Cafferel, M., and Ceperley, D. M. 1992. A Bayesian analysis of Green's function Monte Carlo correlation functions. J. Chem Phys., 97, 8415.
Camp, W. J., and Fisher, M. E. 1972. Decay of order in classical many-body systems I: introduction and formal theory. Phys. Rev. B., 6, 946.
Cardy, J. 1996. Scaling and Renormalization in Statistical Physics. Cambridge University Press.
Carlson, J., Gubernatis, J. E., Ortiz, G., and Zhang, S. 1999. Issues and observations on applications of the constrained-path Monte Carlo method to many-fermion systems. Phys. Rev. B., 59, 12788.
Ceperley, D. M., and Bernu, B. 1988. The calculation of excited state properties with quantum Monte Carlo. J. Chem. Phys., 89, 6316.
Chandrasekharan, S., Cox, J., and Wiesse, U.-J. 1999. Meron cluster solution of fermion sign problems. Phys. Rev. Lett., 83, 3116.
Chandrasekharan, S., Cox, J., Osborn, J. C., and Wiesse, U.-J. 2003. Meron cluster approach to systems of strongly correlated electrons. Nucl. Phys. B, 673, 405.
Changlani, H. J., Kinder, J. M., Umrigar, C. J., and Chan, G. K.-L. 2009. Approximating strongly correlated wave functions with correlator product states. Phys. Rev. B, 80, 245116.
Cirac, J. I., and Verstraete, F. 2009. Renormalization and tensor product states in spin chains and lattices. J. Phys. A: Math. Theor., 42, 504004.
Coldwell, R. L. 1977. Zero Monte Carlo calculations or quantum mechanics is easier. Int. J. Quant. Chem. Symp., 11, 215.
Corboz, P., Jordan, J., and Vidal, G. 2010a. Simulation of fermionic lattice models in two spatial dimensions with fermionic projected entangled pairs: next-nearest neighbor Hamiltonians. Phys. Rev. B, 82, 245119.
Corboz, P., Orus, R., Bauer, B., and Vidal, G. 2010b. Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled pairs. Phys. Rev. B, 81, 165104.
Costi, T. A. 2000. Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys. Phys. Rev. Lett., 85, 1504–1507.
Courant, R., and Hilbert, D. 1965. Methods of Mathematical Physics. Vol. 1. New York: Interscience.
Creutz, M. 1980. Monte Carlo study of quantized SU(2) gauge theory. Phys. Rev. D, 21, 2308.
de Oliveira, P. M. C., Penna, T. J. P., and Herrmann, H. J. 1998a. Broad histogram Monte Carlo. Braz. J. Phys., 26, 677.
de Oliveira, P. M. C., Penna, T. J. P., and Herrmann, H. J. 1998b. Broad histogram Monte Carlo. Eur. Phys. J. B, 1, 205.
Dukelsky, J., Martin-Delgado, M. A., Nishino, T., and Sierra, G. 1998. Equivalence of the variational matrix product method and the density-matrix renormalization group applied to spin chains. Europhys. Lett., 43, 457.
Edegger, B., Muthukumar, V. N., and Gros, C. 2007. Gutzwiller-RVB theory of high temperature superconductivity: results from renormalized mean field theory and variational Monte Carlo calculations. Adv. Phys., 56, 927.
Enz, C. P. 1992. A Course on Many-Body Theory Applied to Solid State Physics. Lecture Notes in Physics, vol. 11. Singapore: World Scientific.
Everett, C. J., and Cashwell, E. D. 1983. A third Monte Carlo sampler. Tech. rept. LA- 9721-MS. Los Alamos National Laboratory.
Evertz, H. G., and Marcu, M. 1994. Page 65 in: Suzuki, M. (ed.), Quantum Monte Carlo Methods in Condensed Matter Physics. Singapore: World Scientific.
Evertz, H. G., Lana, G., and Marcu, M. 1993. Cluster algorithm for vertex models. Phys. Rev. Lett., 70, 875.
Fahy, S. B., and Hamann, D. R. 1990. Positive-projection Monte Carlo simulation: a new variational approach to strongly interacting fermion systems. Phys. Rev. Lett., 65, 3437.
Fahy, S. B., and Hamann, D. R. 1991. Diffusive behavior of states in the Hubbard- Stratonovich transformation. Phys. Rev. B, 43, 765.
Fazekas, P. 1999. Lecture Notes on Electron Correlation and Magnetism. Singapore: World Scientific.
Fazekas, P., and Anderson, P. W. 1974. Ground state properties of anisotropic triangular antiferromagnets. Phil. Mag., 30, 423.
Ferrenberg, A. M., and Swendsen, R. H. 1988. New Monte Carlo technique for studying phase transitions. Phys. Rev. Lett., 61, 2635.
Fetter, A. L., and Walecka, J. D. 1971. Quantum Theory of Many-Particle Systems. New York: McGraw-Hill.
Feynman, R. P., and Hibbs, A. R. 1965. Quantum Mechanics and Path Integrals. New York: McGraw-Hill.
Fisher, M. E., and Barber, M. N. 1972. Scaling theory for finite-size effects in critical region. Phys. Rev. Lett., 28, 1516.
Fishman, G. S. 1996. Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer-Verlag.
Fortuin, C. M., and Kasteleyn, P. W. 1972. Random cluster model. 1. Introduction and relation to other models. Physica, 57, 536.
Friel, N., and Wyse, J. 2012. Estimating the evidence: a review. Statistica Neerlandica, 66, 288.
Fuchs, S., Pruschke, T., and Jarrell, M. 2010. Analytic continuation of quantum Monte Carlo data by stochastic analytic inference. Phys. Rev. E, 81, 56701.
Fuchs, S., Gull, E., Pollet, L., Burovski, E., Kozik, E., Pruschke, T., and Troyer, M. 2011. Thermodynamics of the 3D Hubbard model on approaching the Néel transition. Phys. Rev. Lett., 106, 030401.
Fukui, K., and Todo, S. 2009. Order-N cluster Monte Carlo method for spin systems with long-range interactions. J. Comp. Phys., 228, 2629.
Fulde, P. 1991. Electron Correlations in Molecules and Solids. Solid-State Sciences, vol. 100. Berlin: Springer-Verlag.
Gammel, J. T., Campbell, D. K., and Loh, E. Y. 1993. Extracting infinite system properties from finite-size clusters: phase randomization boundary condition averaging. Synthetic Metals, 57, 4437.
Gelbard, E., and Gu, A. G. 1994. Biases in Monte Carlo eigenvalue calculations. Nuclear Science and Engineering, 117, 1.
Georges, A., Kotliar, G., Krauth, W., and Rozenberg, M. J. 1996. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys., 68, 13.
Geyer, C. J. 1991. Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface. American Statistical Association, vol. 156, New York: American Statistical Association.
Giamarchi, T., and Lhuillier, C. 1990. Variational Monte Carlo study of incommensurate antiferromagnetic phases in the two-dimensional Hubbard model. Phys. Rev. B, 42, 10641.
Giamarchi, T., and Lhuillier, C. 1991. Phase diagrams of the two-dimensional Hubbard and tJ models by a variational Monte Carlo method. Phys. Rev. B, 43, 12943.
Goldstone, J. 1961. Field theories with superconductor solutions. Nuovo Cimento, 19, 154.
Golub, G. H., and Loan, C. F. Van. 1989. Matrix Computations. Baltimore, MD: Johns Hopkins University Press.
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., and Bloch, I. 2002. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature, 415, 39.
Gros, C. 1988. Superconductivity in correlated wave functions. Phys. Rev. B, 38, 931.
Gubernatis, J. E.Editor's note to “Proof of validity of Monte Carlo method for canonical averaging” by M. Rosenbluth. The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm. ed. J. E., Gubernatis, AIP Conference Proceedings, 690, 31 (2003). New York: American Institute of Physics.
Gubernatis, J. E. 2012. Unpublished manuscript.
Gubernatis, J. E., and Booth, T. E. 2008. Multiple extremal eigenvalues by the power method. J. Comp. Phys., 227, 8508.
Gubernatis, J. E., and Zhang, X. Y. 1994. Negative weights in quantum Monte Carlo simulations at finite temperatures using the auxiliary field method. Intl. J. Mod. Phys. C, 8, 590.
Gubernatis, J. E., Hirsch, J. E., and Scalapino, D. J. 1987. Spin and charge corelations around an Anderson magnetic impurity. Phys. Rev. B, 35, 8478.
Gull, E.,Werner, P., Millis, A. J., and Troyer, M. 2007. Performance analysis of continuoustime solvers for quantum impurity models. Phys. Rev. B, 76, 235123.
Gull, E., Werner, P., Parcollet, O., and Troyer, M. 2008. Continuous-time auxiliary-field Monte Carlo for quantum impurity models. Europhys. Lett., 82, 57003.
Gull, E., Millis, A. J., Lichtenstein, A. I., Rubtsov, A. N., Troyer, M., and Werner, P. 2011. Continuous-timeMonte Carlo methods for quantum impurity models. Rev. Mod. Phys., 83, 349.
Gull, S. F., and Skilling, J. 1984. Maximum entropy image reconstruction. IEE Proc., 131F, 646.
Gutzwiller, M. C. 1965. Effect of correlation on the ferromagnetism of transition metals. Phys. Rev. Lett., 10, 159.
Hamann, D. R., and Fahy, S. B. 1990. Energy measurement in auxiliary-field many-electron calculations. Phys. Rev. B, 41, 11352.
Hammond, B. L., W. A., LesterJr., and Reynolds, P. J. 1994. Monte Carlo Methods in ab Initio Quantum Chemistry. Singapore: World Scientific.
Handscomb, D. C. 1962a. A Monte Carlo method applied to the Heisenberg ferromagnet. Proc. Cambridge Philos. Soc., 58, 594.
Handscomb, D. C. 1962b. The Monte Carlo method in quantum statistical mechanics. Proc. Cambridge Philos. Soc., 58, 594.
Harada, K., and Kawashima, N. 2001. Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions. J. Phys. Soc. Jpn., 70, 13.
Harada, K., and Kawashima, N. 2002. Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems. Phys. Rev. E., 66, 056705.
Harada, K., Troyer, M., and Kawashima, N. 1998. The two-dimensional S= 1 quamtum Heisenberg antiferromagnet at finite temperatures. J. Phys. Soc. Jpn., 67, 1130.
Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97.
Hatano, N., and Suzuki, M. 1992. Representation basis in quantum Monte Carlo calculations and the negative-sign problem. Phys. Lett. A, 163, 246.
Hatano, N., and Suzuki, M. 2005. Finding exponential product formulas of higher orders. Lect. Notes Phys., 679, 37.
Haule, K. 2007. Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base. Phys. Rev. B, 75, 155113.
Haule, K. 2015. Exact Double Counting in Combining the Dynamical Mean Field Theory and the Density Functional Theory. Phys. Rev. Lett., 115, 196403.
Hettler, M. H., Tahvildar-Zadeh, A. N., Jarrell, M., Pruschke, T., and Krishnamurthy, H. R. 1998. Nonlocal dynamical correlations of strongly interacting electron systems. Phys. Rev. B, 58, R7475.
Himeda, A., and Ogata, M. 2000. Spontaneous deformation of the Fermi surface due to strong correlation in the two-dimensional tJmodel. Phys. Rev. Lett., 85, 4345.
Himeda, A., Kato, T., and Ogata, M. 2002. Stripe states with spatially oscillating d-wave superconductivity in the two-dimensional tt_Jmodel. Phys. Rev. Lett., 88, 117001.
Hirsch, J. E. 1983. Discrete Hubbard-Stratonovich transformation for fermion lattice models. Phys. Rev. B, 28, 1983.
Hirsch, J. E. 1985. Two-dimensional Hubbard model. Phys. Rev. B, 31, 4403.
Hirsch, J. E. 1987. Simulations of the three-dimensional Hubbard model: half-filled band sector. Phys. Rev. B, 35, 1851.
Hirsch, J. E., and Fye, R. M. 1986. Monte Carlo method for magnetic impurities in metals. Phys. Rev. Lett., 56, 2521.
Hoshen, J., and Kopelman, R. 1976. Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm. Phys. Rev. B, 14, 3438.
Householder, A. S. 2006. The Theory of Matrices in Numerical Analysis. New York: Dover.
Hukushima, K., and Nemoto, K. 1996. Exchange Monte Carlo method and application to spin glass simulations. J. Phys. Soc. Jpn., 65, 1604.
Huscroft, C., Gross, R., and Jarrell, M. 2000. Maximum entropy method of obtaining thermodynamic properties from quantum Monte Carlo simulations. Phys. Rev. B, 61, 9300.
Iazzi, M., and Troyer, M. 2014. Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models. arXiv:1411. 0683.
Janke, W., and Kappler, S. 1995. Multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions. Phys. Rev. Lett., 74, 212.
Jarrell, M., and Gubernatis, J. E. 1996. Bayesian inference and the analytic continuation of quantum Monte Carlo data. Phys. Rept., 269, 133.
Jarrell, M., Macridin, A., Mikelsons, K., Doluweera, D. G. S. P., and Gubernatis, J. E.The dynamical cluster approximation with quantum Monte Carlo cluster solvers.” AIP Conference Proceedings, 1014, 24. (2008).
Jordan, P., and Wigner, E. 1928. Über das Paulische Äquivalenzverbot. Zeit. Phys., 47, 631.
Kalos, M. H., and Pederiva, F. 2000. Exact Monte Carlo for continuum fermion systems. Phys. Rev. Lett., 85, 3547.
Kalos, M. H., and Whitlock, P. A. 1986. Monte Carlo Methods I: Basics. New York: Wiley-Interscience.
Karlin, S., and Taylor, H.W. 1975. A First Course in Stochastic Processes. Academic Press.
Kashurnikov, V. A., Prokof'ev, N. V., Svistunov, B. V., and Troyer, M. 1999. Quantum spin chains in a magnetic field. Phys. Rev. B, 59, 1162.
Kasteleyn, P.W., and Fortuin, C. M. 1969. Phase transitions in lattice systems with random local properties. J. Phys. Soc. Jpn. Suppl., 26, 11.
Kato, Y., and Kawashima, N. 2009. Quantum Monte Carlo method for the Bose-Hubbard model with harmonic confining potential. Phys. Rev. E, 79, 021104.
Kato, Y., and Kawashima, N. 2010. Finite-size scaling for quantum criticality above the upper critical dimension: superfluid–Mott-insulator transition in three dimensions. Phys. Rev. E, 81, 011123.
Kaul, R. 2007. Private communication.
Kawashima, N. 1996. Cluster algorithms for anisotropic quantum spin models. J. Stat. Phys., 82, 131.
Kawashima, N. 2007. Unpublished manuscript.
Kawashima, N., and Gubernatis, J. E. 1994. Loop algorithms for Monte Carlo simulations of quantum spin systems. Phys. Rev. Lett., 73, 1295.
Kawashima, N., Evertz, H., and Gubernatis, J. E. 1994. Loop algorithms for quantum simulations of fermions on lattices. Phys. Rev. B, 50, 136.
Kawashima, N., Jarrell, M., and Gubernatis, J. E. 1996. Cluster Monte Carlo study of the quantum XY model in two dimensions. Int. J. Mod. Phys. C, 7, 433.
Khinchin, A. I. 1957. Mathematical Foundations of Information Theory. New York: Dover.
Kim, D. Y., and Chan, M. H. W. 2012. Absence of supersolidity in solid helium in porous Vycor glass. Phys. Rev. Lett., 109, 155301.
Knuth, D. E. 1997. The Art of Computer Programming, vol. 2: Seminumerical Algorithms, third ed. Reading: Addison Wesley. Page 119.
Kotliar, G., Savrasov, S. Y., Haule, K., Oudovenko, V. S., Parcollet, O., and Marianetti, C. A. 2006. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys., 78, 865.
Kuklov, A. B., and Svistunov, B. V. 2003. Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice. Phys. Rev. Lett., 90, 100401.
Kuklov, A. B., Prokof'ev, N., and Svistunov, B. V. 2004. Commensurate two-component bosons in an optical lattice: ground state phase diagram. Phys. Rev. Lett., 92, 050402.
Landau, D. P., and Binder, K. 2000. A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press.
Läuchli, A. M., and Werner, P. 2009. Krylov implementation of the hybridization expansion impurity solver and application to 5-orbital models. Phys. Rev. B, 80, 235117.
Li, Z.-X., Jiang, Y.-F., and Yao, H. 2014. Solving fermion sign problem in quantum Monte Carlo by Majorana representation. arXiv:1408. 2269.
Liang, S., Doucot, D., and Anderson, P. W. 1988. Some new variational resonating valence bond type wave functions for the spin antiferromagnetic Heisenberg model on a square lattice. Phys. Rev. Lett., 61, 365.
Lichtenstein, A. I., and Katsnelson, M. I. 2000. Antiferromagnetism and d-wave superconductivity in cuprates: a cluster dynamical mean-field theory. Phys. Rev. B, 62, R9283.
Lin, C., Zong, F. H., and Ceperley, D. M. 2001. Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys. Rev. E, 64, 016702.
Lin, X., Zhang, H., and Rappe, A. M. 2000. Optimization of quantum Monte Carlo wave functions using analytical energy derivatives. J. Chem. Phys., 112, 2650.
Liu, J. S. 2001. Monte Carlo Strategies for Scientific Computing. New York: Springer-Verlag.
Loh, E. Y.Jr., and Gubernatis, J. E. 1992. Stable numerical simulations of models of interacting electrons in condensed-matter physics. Chap. 4 of: Hanke,W., and Kopaev, Yu. V. (eds.). Electronic Phase Transitions. Modern Problems in Condensed-Matter Physics, vol. 32. Amsterdam: North-Holland.
Loh, E. Y.Jr., Gubernatis, J. E., Scalettar, R. T., Sugar, R. L., and White, S. R. 1989. Stable matrix-multiplication algorithms for the low-temperature numerical simulation of fermions. Page 55 of: Baeriswyl, D., and Campbell, D. K. (eds.). Interacting Electrons in Reduced Dimensions. NATO ASI Series, vol. 213. New York: Plenum.
Loh, E. Y.Jr., Gubernatis, J. E., Scalettar, R. T., White, S. R., Scalapino, D. J., and Sugar, R. L. 1990. Sign problem in the numerical simulation of many-electron systems. Phys. Rev. B, 41, 9301.
Loh, E. Y.Jr., Gubernatis, J. E., Scalettar, R. T., White, S. R., Scalapino, D. J., and Sugar, R. L. 2005. Numerical stability and the sign problem in the determinant quantum Monte Carlo method. Int. J. Mod. Phys. C, 16, 1319.
Luijten, E., and Blöte, H.W. J. 1995. Monte Carlo method for spin models with long-range interactions. Int. J. Mod. Phys. C, 6, 359.
Ma, S.-K. 1985. Modern Theory of Critical Phenomena. Singapore: World Scientific.
Maier, T., Jarrell, M., Pruschke, T., and Hettler, M. H. 2005. Quantum cluster theories. Rev. Mod. Phys., 77, 1027.
Majumdar, D. K., and Ghosh, C. K. 1969a. On nearest-neighbor interaction in linear chain: I. J. Math. Phys., 10, 1388.
Majumdar, D. K., and Ghosh, C. K. 1969b. On nearest-neighbor interaction in linear chain: II. J. Math. Phys., 10, 1399.
Marinari, E., and Parisi, G. 1992. Simulated tempering: a new Monte Carlo scheme. Europhys. Lett., 19, 451.
Marshall, W. 1955. Antiferromagetism. Proc. Roy. Soc. (London) A, 232, 48.
Marti, K., Bauer, B., Reiher, M., Troyer, M., and Verstraete, F. 2010. Complete-graph tensor network states: a new fermionic wavefunction for molecules. New J. Phys., 12, 103008.
Marzari, N., and Vanderbilt, D. 1997. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B, 56, 12847.
Masaki, A., Suzuki, T., Harada, K., Todo, S., and Kawashima, N. 2013. Parallelized quantum Monte Carlo algorithm with non-local worm update. Phys. Rev. Lett. 112, 140603 (2014).
Masaki-Kato, A., Suzuki, T., Harada, K., Todo, S., and Kawashima, N. 2014. Parallelized quantum Monte Carlo algorithm with nonlocal worm updates. Phys. Rev. Lett., 112, 140603.
Matsubara, T., and Masuda, H. 1956. A lattice model of liquid helium. Prog. Theor. Phys., 16, 416.
McCulloch, I. 2007. From density-matrix renormalization group to matrix product states. J. Stat. Mech., P10014.
McQueen, P. G., and Wang, C. S. 1991. Variational Monte Carlo evaluation of Gutzwiller states for the Anderson lattice model. Phys. Rev. B, 44, 10021.
Metropolis, N. 1985. Monte Carlo: in the beginning and some great expectations. Page 62 of: Alcouffe, R., et al. (eds.). Monte Carlo Calculations and Applications in Neutronics, Photonics, and Statistical Physics. Berlin: Springer-Verlag.
Metropolis, N. 1987. The beginning of the Monte Carlo method. Los Alamos Science, Special Issue, 125.
Metropolis, N., and Ulam, S. 1949. The Monte Carlo method. J. Am. Stat. Assoc., 44, 335.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, A. 1953. Equations of state by fast computing machines. J. Chem. Phys., 21, 1087.
Metzner, W., and Vollhardt, D. 1989. Correlated lattice fermions in d-dimensions. Phys. Rev. Lett., 62, 324.
Meyer, C. D. 2000. Matrix Analysis and Applied Linear Algebra Research. Philadelphia: SIAM.
Mezzacapo, F. 2011. Variational study of a mobile hole in a two-dimensional quantum antiferromagnet using entangled-plaquette states. Phys. Rev. B, 83, 115111.
Mezzacapo, F., Schuch, N., Boninsegni, M., and Cirac, J. I. 2009. Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo. New J. Phys., 11, 83026.
Mikelsons, K., Macridin, A., and Jarrell, M. 2009. Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods. Phys. Rev. E, 79, 057701.
Moskowitz, J. W., Schmidt, K. E., Lee, M. A., and Kalos, M. H. 1982. A new look at correlation energy in atomic and molecular systems. II: the application of the Green's function Monte Carlo method to LiH. J. Chem. Phys., 77, 349.
Muramatsu, A., Zumbach, G., and Zotos, X. 1992. A geometric view of the minus-sign problem. Int. J. Modern Phys. C, 3, 185.
Nambu, Y. 1960. Quasiparticles and gauge invariance in the theory of superconductivity. Phys. Rev., 117, 648.ndash;663.
Nave, C. P., Ivanov, D. A., and Lee, P. A. 2006. Variational Monte Carlo study of the current carried by a quasiparticle. Phys. Rev. B, 73, 104502.
Negele, J.W., and Orland, H. 1988. Quantum Many-Particle Systems. New York: Addison- Wesley.
Neuscamman, E., Changlani, H., Kinder, J. M., and Chan, G. K.-L. 2011. Nonstochastic algorithms for Jastrow-Slater and correlator product state wavefunctions. Phys. Rev.B, 84, 205132.
Neuscamman, E., Umrigar, C. J., and Chan, G. K.-L. 2012. Optimizing large parameter set in variational quantum Monte Carlo. Phys. Rev. B, 85, 045103.
Newman, M. E. J., and Barkema, G. T. 1999. Monte Carlo Methods in Statistical Physics. New York: Oxford University Press.
Nielsen, M. A., and Chaung, I. L. 2000. Quantum Computation and Quantum Information. Cambridge University Press.
Nightingale, M. P. 1999. Basics, quantum Monte Carlo, and statistical mechanics. In:
Nightingale, M. P., and Umrigar, C. J. (eds.). Quantum Monte Carlo Methods in Physics and Chemistry. NATO Science Series, vol. 525. Dordrecht: Kluwer.
Nightingale, M. P., and Melik-Alaverdian, V. 2001. Optimization of ground and excited states wave functions and van der Waals clusters. Phys. Rev. Lett., 87, 43401.
Nishimori, H., and Ortiz, G. 2010. Elements of Phase Transitions and Critical Phenomena. Oxford University Press.
Oguri, A., and Asahata, T. 1992. Brinkman-Rice transition in the three-band Hubbard model. Phys. Rev. B, 46, 14073.
Oguri, A., Asahata, T., and Maekawa, S. 1994. Gutzwiller wave function in the three-band Hubbard: a variational Monte Carlo study. Phys. Rev. B, 49, 6880.
Ohgoe, T.Suzuki, T. and Kawashima, N. 2012. Commensurate supersolid of threedimensional lattice bosons. Phys. Rev. Lett., 108, 185302.
Ortiz, G., Ceperley, D. M., and Martin, R. M. 1993. New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field. Phys. Rev. Lett., 71, 2777.
Ortiz, G., Gubernatis, J. E., and Carlson, J. A. 1997. Stochastic approach to lattice fermions in a magnetic field. Bull. Am. Phys. Soc., March Meeting, M11.10.
Ostlund, S., and Rommer, S. 1995. Thermodynamic limit of density-matrix renormalization. Phys. Rev. Lett., 75, 3557.
Otsuki, J., Kusunose, H., Werner, P., and Kuramoto, Y. 2007. Continuous-time quantum Monte Carlo method for the Coqblin–Schrieffer model. J. Phys. Soc. Japan, 76, 114707.
Paramekanti, A., Randeria, M., and Trivedi, N. 2001. Projected wave functions and high temperature superconductivity. Phys. Rev. Lett., 87, 217002.
Parisi, G. 1988. Statistical Field Theory. Frontiers in Physics, vol. 66. New York: Addison Wesley.
Peskun, P. H. 1973. Optimum Monte Carlo sampling using Markov chains. Biometrika, 60, 607.
Pollock, E. L., and Ceperley, D. M. 1987. Path-integral computation of superfluid densities. Phys. Rev. B, 36, 8343.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. 2007. Numerical Recipes: The Art of Scientific Computing, third edition. Cambridge University Press.
Prokof'ev, N., and Svistunov, B. 2001. Worm algorithms for classical statistical models. Phys. Rev. Lett., 87, 160601.
Prokov'ev, N. V., Svistunov, B. V., and Tupitsyn, I. S. 1998. Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems. Sov. Phys. JETP, 87, 310.
Purwanto, W., and Zhang, S. 2004. Quantum Monte Carlo for the ground state of many bosons. Phys. Rev. B, 70, 056702.
Renyi, A. 1960. On measures of entropy and information. Page 547 of: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press.
Reynolds, P. J., Ceperley, D. M., Alder, B. J., and Lester, W. A. 1982. Fixed-node Monte Carlo for molecules. J. Chem. Phys., 77, 5593.
Rieger, H., and Kawashima, N. 1999. Application of a continuous time cluster algorithm to the two-dimensional random quantum Ising ferromagnet. Eur. Phys. J. B, 9, 233.
Rombouts, S., Heyde, K., and Jachowicz, N. 1999a. A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions.Phys. Lett., 82, 4155.
Rombouts, S. M. A., Heyde, K., and Jachowicz, N. 1999b. Quantum Monte Carlo method for fermions, free of discretization errors. Phys. Rev. Lett., 82, 4155.
Rosenbluth, M. 1953. Proof of validity of Monte Carlo method for canonical averaging. Tech. rept. LADC-1567 (AECU-2773). Los Alamos National Laboratory.
Rosenbluth, M. N. “Genesis of the Monte Carlo algorithm for statisitcal mechanics,” in The Monte Carlo Method in the Physical Sciences:Celebrating the 50th Anniversary of the Metropolis Algorithm, ed. J. E., Gubernatis, AIP Conference Proceedings, 690, 22 (2003). New York: American Institute of Physics.
Rubenstein, B. M., Gubernatis, J. E., and Doll, J. D. 2010. Comparative Monte Carlo efficiency by Monte Carlo analysis. Phys. Rev. E, 82, 36701.
Rubtsov, A. N., Savkin, V. V., and Lichtenstein, A. I. 2005. Continuous-time quantum Monte Carlo method for fermions. Phys. Rev. B, 72, 035122.
Sachdev, S. 1999. Quantum Phase Transitions. New York: Cambridge University Press.
Samson, J. H. 1993. Quantum Monte Carlo computation: the sign problem as a Berry phase. Phys. Rev. Lett., 47, 3408.
Samson, J. H. 1995. Auxiliary fields and the sign problem. Int. J. Modern Phys. C, 6, 427.
Sandvik, A. 2008. Scale-renormalized matrix-product states for correlated quantum systems.Phys. Rev. Lett., 101, 140603.
Sandvik, A. W. 1992. A generalization of Handscomb's quantum Monte Carlo schemeapplication to the 1D Hubbard mode. J. Phys. A: Math. Gen., 25, 3667.
Sandvik, A. W. 1999. Stochastic series expansion method with operator-loop update. Phys. Rev. B, 59, 14157.
Sandvik, A. W., and Evertz, H. G. 2010. Loop updates and projector quantum Monte Carlo in the valence bond basis. Phys. Rev. B, 82, 024407.
Sandvik, A.W., and Kurkijärvi, J. 1991. Quantum Monte Carlo simulation method for spin systems. Phys. Rev. B, 43, 5950.
Sandvik, A. W., and Vidal, G. 2007. Variational Monte Carlo simulations with tensornetwork states.Phys. Rev. Lett., 99, 220602.
Sarsa, A., Fatoni, S., Schmidt, K. E., and Pederiva, F. 2003. Neutron matter at zero temperature with the auxiliary-field diffusion Monte Carlo method. Phys. Rev. C, 68, 024308.
Scalapino, D. J., and Sugar, R. L. 1981. Method for performing Monte Carlo calculations for systems with fermions. Phys. Rev. Lett., 46, 519.
Scalettar, R. T., Scalapino, D. J., Sugar, R. L., and Toussaint, D. 1987. Hybrid Monte Carlo for the numerical simulation of many-electron systems. Phys. Rev. B, 36, 8632.
Scalettar, R. T., Noack, R. M., and Singh, R. P. 1991. Ergodicity at large couplings with the determinant Monte Carlo algorithm. Phys. Rev. B, 44, 10502.
Schautz, F., and Filippi, C. 2004. Optimized Jastrow-Slater wave functions for ground and excited states: application to the lowest states of ethene. J. Chem. Phys., 120, 10931.
Schmidt, K. E., and Fantoni, S. 1999. A quantum Monte Carlo method for nucleon systems. Phys. Lett., B446, 99.
Schmidt, K. E., Sarsa, A., and Fatoni, S. 2001. A constrained path Monte Carlo for nucleon systems. Int. J. Mod. Phys. B, 15, 1510.
Schmidt, K. E., Fatoni, S., and Sarsa, A. 2003. Constrained path calculation of the 4He and 16O nuclei. Eur. J. Phys., A17, 469.
Schollwöck, U. 2005. The density matrix renormalization group. Rev. Mod. Phys., 77, 259.
Schrödinger, E. 1952. Statistical Thermodynamics. Cambridge University Press.
Sfondrini, A., Cerrillo, J., Schuch, N., and Cirac, J. I. 2010. Simulating two- and threedimensional frustrated quantum systems with string-bond states. Phys. Rev. B, 81, 214426.
Schuch, N., Wolf, M. M., Verstraete, F., and Cirac, J. I. 2008. Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions. Phys. Rev. Lett., 100, 40501.
Shi, H., and Zhang, S. 2013. Symmetry in auxiliary-field quantum Monte Carlo calculations. Phys. Rev. B, 88, 125132.
Shiba, H. 1986. Properties of strongly correlated Fermi liquid in valence fluctuation system – a variational Monte Carlo study. J. Phys. Soc. Japan, 55, 2765.
Shiba, H., and Fazekas, P. 1990. Correlated Fermi-liquid state formed with overlapping Kondo clouds. Prog. Theor. Phys. Suppl., 101, 403.
Shore, J. E., and Johnson, R. W. 1980. Axiomatic derivation of the principle of maximum entropy and of minimum cross-entropy. IEEE Trans. Inform. Theory, IT-26, 26.
Shore, J. E., and Johnson, R. W. 1983. Comments on and corrections to “Axiomatic derivation of the principle of maximum entropy and of minimum cross-entropy.” IEEE Trans. Inform. Theory, IT-29, 942.
Sivia, D. S., and Skilling, J. 2006. Data Analysis: A Bayesian Tutorial. Oxford University Press.
Skilling, J. 1998. Massive inference and maximum entropy. In: Fischer, R., Preuss, R., and von Toussaint, U. (eds.), Maximum Entropy and Bayesian Methods. Dordrecht: Kluwer.
Sorella, S. 1998. Green function Monte Carlo with stochastic reconfiguration. Phys. Rev. Lett., 80, 4558.
Sorella, S. 2000. Green function Monte Carlo with stochastic reconfiguration: an effective remedy for the sign problem. Phys. Rev. B, 61, 2599.
Sorella, S. 2005. Wave function optimization in the variational Monte Carlo method. Phys. Rev. B, 71, 241103.
Sorella, S., Baroni, S., Car, R., and Parrinello, M. 1989. A novel technique for the simulation of interacting fermion systems. Eurphys. Lett., 8, 663.
Sorella, S., Martins, G. B., Becca, F., Gazza, C., Capriotti, L., Parola, A., and Dagotto, E. 2002. Superconductivity in the two-dimensional tJ model. Phys. Rev. Lett., 88, 117002.
Spanier, J., and Gelbard, E. M. 1969. Monte Carlo Principles and Neutron Transport Problems. Reading, MA: Addison-Wesley.
Stewart, G. W. 2001a. Matrix Algorithms I: Basic Decompositions. Philadelphia: SIAM.
Stewart, G. W. 2001b. Matrix Algorithms II: Eigensystems. Philadelphia: SIAM.
Sugiyama, G., and Koonin, S. E. 1986. Auxiliary field Monte Carlo for quantum manybody ground states. Ann. Phys., 168, 1.
Surer, B., Troyer, M., Werner, P., Wehling, T. O., Läuchli, A. M., Wilhelm, A., and Lichtenstein, A. I. 2012. Multiorbital Kondo physics of Co in Cu hosts. Phys. Rev.B, 85, 085114.
Suzuki, M. 1976a. Generalized Trotter's formula and systematic approximants of exponential operators and inner derivatives with applications to many-body problems.Comm. Math. Phys., 51, 183.
Suzuki, M. 1976b. Relationship between d-dimensional quantal spin systems and (d + 1)- dimensional Ising systems: equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. of Theor. Phys., 56, 1454.
Swendsen, R. H., and Wang, J.-S. 1987. Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58, 86.
Sylju°asen, O. F. 2008. Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations. Phys. Rev. B, 78, 174429.
Sylju°asen, O. F., and Sandvik, A. W. 2002. Quantum Monte Carlo with directed loops. Phys. Rev. E, 66, 046701.
Tahara, D., and Imada, M. 2008. Variational Monte Carlo method with quantum number projection and multi-variable optimization. J. Phys. Soc. Japan, 77, 114701.
Takasaki, H., Hikihara, T., and Nishino, T. 1999. Fixed point of the finite system DMRG. J. Phys. Soc. Japan, 68, 1537.
ten Haaf, D. F. B., Bemmel, H. J. M., van Leeuwen, J. M. J., van Saarlos, W., and Ceperley, D. 1995. Proof of upper bound in fixed-node Monte Carlo for lattice fermions. Phys. Rev. B, 51, 13039.
Thompson, C. P. 1972. Mathematical Statistical Mechanics. Princeton, NJ: Princeton University Press.
Thouless, D. J. 1961. The Quantum Mechanics of Many-Body Systems. New York: Academic.
Todo, S., and Kato, K. 2001. Cluster algorithms for general-S quantum spin systems. Phys. Rev. Lett., 87, 047203.
Todo, S., Matsuo, H., and Shitara, H. 2012. Private communication.
Toulouse, J., and Umrigar, C. J. 2007. Optimization of quantum many-body wave function by energy minimization.J. Chem. Phys., 126, 84102.
Toulouse, J., and Umrigar, C. J. 2008. Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic atoms. J. Chem. Phys., 128, 174101.
Trotzky, S., Pollet, L., Gerbier, F., Schnorrberger, U., Bloch, I., Prokof'ev, N. V., Svistunov, B., and Troyer, M. 2010. Suppression of the critical temperature for superfluidity near the Mott transition. Nature Physics, 6, 998.
Troyer, M., Wessel, S., and Alet, F. 2003. Flat histogram methods for quantum systems: algorithms to overcome tunneling problems and calculate the free energy. Phys. Rev. Lett., 90, 120201.
Umrigar, C. J., and Filippi, C. 2005. Energy and variance optimization of many-body wave functions. Phys. Rev. Lett., 94, 150201.
Umrigar, C. J., Wilson, K. G., and Wilkins, J. W. 1988. Optimized trial wave functions for quantum Monte Carlo calculations. Phys. Rev. Lett., 60, 1719.
Umrigar, C. J., Toulouse, J., Filippi, C., Sorella, S., and Hennig, R. G. 2007. Alleviation of the fermion-sign problem by optimization of many-body wave functions. Phys. Rev. Lett., 98, 110202.
van Hove, L. 1950. Sur l'integrale de configuration pour les systemémes de particules á une dimension. Physica, XVI, 137.
Verstraete, F., Murg, V., and Cirac, J. I. 2008. Matrix product states, projected entangled pair state, and variational renormalization group methods for quantum spin systems. Adv. Phys., 37, 143.
Walker, A. J. 1977. An efficient method for generating discrete random variables with general distributions. ACM Trans. Math. Softw., 3, 253.
Wang, F., and Landau, D. P. 2001. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett., 86, 2050.
Wang, J.-S., Tay, T. K., and Swendsen, R. H. 1999. Transition matrix Monte Carlo reweighting and dynamics. Phys. Rev. Lett., 82, 476.
Wang, L., Pizorn, I., and Verstraete, F. 2011a. Monte Carlo simulation with tensor network states. Phys. Rev. B, 2011, 134421.
Wang, L., Kao, Y.-J., and Sandvik, A. W. 2011b. Plaquette renormalization scheme for tensor network states. Phys. Rev. E 83, 056703 (2011).
Wang, L., Iazzi, M., Corboz, P., and Troyer, M. 2015. Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions. Phys. Rev. B 91, 235151 (2015).
Watanabe, H., and Ogata, M. 2009. Fermi surface reconstruction in the periodic Anderson model. J. Phys. Soc. Japan, 78, 024715.
Watanabe, T., Yokoyama, H., Tanaka, Y., and Inoue, J. I. 2006. Superconductivity and a Mott transition in a Hubbard model on an anisotropic triangular lattice. J. Phys. Soc. Japan, 75, 074707.
Weber, C., Läuchli, A.,Mila, F., and Giamarchi, T. 2006. Magnetism and superconductivity of strongly correlated electrons on the triangular lattice. Phys. Rev. B, 73, 014519.
Werner, P., and Millis, A. J. 2006. Hybridization expansion impurity solver: general formulation and application to Kondo lattice and two-orbital models. Phys. Rev. B, 74, 155107.
Werner, P., and Millis, A. J. 2007. High-spin to low-spin and orbital polarization transitions in multiorbital Mott systems. Phys. Rev. Lett., 99, 126405.
Werner, P., Comanac, A., de' Medici, L., Troyer, M., and Millis, A. J. 2006. Continuoustime solver for quantum impurity models. Phys. Rev. Lett., 97, 076405.
White, S. R. 1992. Density-matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69, 2863.
Wilson, K. G. 1975. The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys., 47, 773.
Wolff, U. 1989. Collective Monte Carlo updating for spin systems. Phys. Rev. Lett., 62, 361.
Wood, W.W., and Parker, F. R. 1957. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. I. A supercritical isotherm at about twice the critical temperature. J. Chem. Phys., 27, 720.
Wu, C. J., and Zhang, S. C. 2005. Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm.Phys. Rev. B, 71, 155115.
Yamaguchi, C., and Kawashima, N. 2002. Combination of improved multibondic method and the Wang-Landau method.Phys. Rev. E., 65, 056710.
Yamaguchi, C., Kawashima, N., and Okabe, Y. 2002. Broad histogram relation for the bond number and its applications. Phys. Rev. E., 66, 036704.
Yanagisawa, T. 1999. Wave functions of correlated electron state in the periodic Anderson model.J. Phys. Soc. Japan, 1999, 893.
Yang, H.-Y., Yang, F., Jiang, Y.-J., and Li, T. 2007. On the origin of the tunneling asymmetry in the cuprate superconductors: a variational perspective.J. Phys.: Condens. Matter, 19, 016217.
Yokoyama, H., and Shiba, H. 1987a. Variational Monte Carlo studies of the Hubbard model. I. J. Phys. Soc. Japan, 56, 1490.
Yokoyama, H., and Shiba, H. 1987b. Variational Monte Carlo studies of the Hubbard model. II. J. Phys. Soc. Japan, 56, 3582.
Yokoyama, H., and Shiba, H. 1988. Variational Monte Carlo studies of superconductivity in strongly correlated electron systems.H. Yokoyama and H. Shiba, 57, 2482.
Yoo, J., Chandrasekharan, S., Kaul, R. K., Ullmo, D., and Baranger, H. U. 2005. On the sign problem in the Hirsch-Fye algorithm for impurity problems. J. Phys. A: Math. Gen., 38, 10307.
Yunoki, S., Dagotto, E., and Sorella, S. 2005. Role of strong correlation in the recent angleresolved photoemission spectroscopy experiments on cuprate superconductors. Phys. Rev. Lett., 94, 037001.
Zhang, S. 2013. Auxiliary-field quantum Monte Carlo for correlated electron systems. In: Pavarini, E., Kock, E., and Schollwöck, U. (eds.), Emergent Phenomena in Correlated Matter Modeling and Simulation, vol. ö. http://hdl.handle.net/2128/5389: Open source.
Zhang, S., and Kalos, M. H. 1991. Exact Monte Carlo for few electron systems. Phys. Rev. Lett., 67, 3074.
Zhang, S., and Krakauer, H. 2003. Quantum Monte Carlo using phase-free random walks with Slater determinants.Phys. Rev. Lett., 90, 136401.
Zhang, S., Carlson, J., and Gubernatis, J. E. 1995. Constrained path Monte Carlo for fermion ground states. Phys. Rev. Lett., 74, 3652.
Zhang, S., Carlson, J., and Gubernatis, J. E. 1997. Constrained path Monte Carlo method for fermion ground states. Phys. Rev. B, 55, 7464.

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