Skip to main content Accessibility help
Quantum Scaling in Many-Body Systems
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 21
  • Export citation
  • Recommend to librarian
  • Buy the print book

Book description

Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.


'The book is instructive, rich, stimulating and easy to follow, providing physical insight to many quantum critical phenomena where traditional theory becomes insufficient. The author draws attention to the physical interpretation and significant implications of the mathematical results presented here. The material is aimed at advanced graduate students in condensed matter or early career researchers … The book is very attractive, readable, containing discussions, comments or explanatory figures whenever is necessary. The author combines easy-to-grasp physical intuitive concepts with relevant mathematical expressions and advanced calculations, allowing the text to flow easily, in a highly organised and unified manner.'

Eric Howard Source: Contemporary Physics

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


Alexandrov, Victor and Coleman, Piers (2014), Phys. Rev. B 90, 115147.
Alicea, Jason (2012), Reports on Progress in Physics, 75, 076501.
Anderson, P. W. (1963), Phys. Rev. 130, 439.
Anderson, P. W. (1970), J. Phys. C: Sol. St. Phys. 3, 2436.
Aubry, S and André, G. (1980), Ann. Israel Phys. Soc. 3, 133.
Auerbach, A. (1994), Interacting Electrons and Quantum Magnetism, New York: Springer-Verlag.
Barber, M. and Batchelor, M. T. (1989) Phys. Rev. B40, 4621.
Bauer, E. D., Yang, Yi-feng, Capan, C., Urbano, R. R., Miclea, C. F., Sakai, H., Ronning, F., Graf, M. J., Balatsky, A. V., Movshovich, R., Bianchi, A. D., Reyes, A. P., Kuhns, P. L., Thompson, J. D. and Fisk, Z. (2011) PNAS 108, 6857.
Beal-Monod, M. T., Ma, S. K. and Fradkin, D. R. (1968), Phys. Rev. Lett. 20, 929.
Belitz, D. and Kirkpatrick, T. R. (1994), Rev. Mod. Phys. 66, 361.
Belitz, D., Kirkpatrick, T. R. and Vojta, T. (2005), Rev. Mod. Phys. 77, 579.
Belitz, D., Kirkpatrick, T. R. and Rollbüler, J. (2005), Phys. Rev. Lett. 94, 247205.
Belvedere, L. (1999), Lecture Notes, Universidade Federal Fluminense, unpublished.
Blanter, Ya. M., Kaganov, M. I., Pantsulaya, A. V., Varlamov, A. A. (1994), Phys. Rep. 245, 159.
Blundell, Stephen (2001), Magnetism in Condensed Matter (Oxford Master Series in Condensed Matter Physics).
Boechat, B., dos Santos, R. R. and Continentino, M. A. (1994), Phys. Rev. B49, R6404.
Bray, A. J. and Moore, M. A. (1985), J. Phys. C: Solid State Phys. 18, L927.
Brézin, E. (2015), in Ken Wilson Memorial Volume: Renormalisation, Lattice Gauge Theory, the Operator Product Expansion and Quantum Fields, Baaquie, B. E., Huang, K., Peskin, M. E. and Phua, K. K. (eds.), World Scientific Publishing Co. Pte. Ltd.
Brinkman, W. F. and Rice, T. M. (1970), Phys. Rev. B2, 4302.
Büttiker, M., Imry, Y., and Landauer, R. (1983), Phys. Lett. A96, 365.
Byers, N. and Yang, C. N. (1961), Phys. Rev. Lett. 7, 46.
Caldas, H. and Continentino, M. A. (2012), Phys. Rev. B86, 144503.
Cardy, J. (1996), Scaling and Renormalization in Statistical Physics, Cambridge University Press.
Castro Neto, A. H., Castilla, G. E. and Jones, B. A. (1998), Phys. Rev. Lett. 81, 3531.
Cestari, J. C. C., Foerster, A. and Gusmão, M. A. (2010), Phys. Rev. A82, 063634.
Cestari, J. C. C., Foerster, A. Gusmão, M. A. and Continentino, M. A. (2011), Phys. Rev. A84, 055601.
Chakravarty, S., Halperin, B. I. and Nelson, D. (1988), Phys. Rev. Lett. 60, 1057.
Chandrasekhar, B. S. (1962) Appl. Phys. Lett. 1, 7.
Clogston, A. M. (1962) Phys.Rev.Lett. 9, 266.
Coleman, P. (1983), Phys. Rev. B28, 5255.
Coleman, S. and Weinberg, E. (1973), Phys. Rev. D7, 1888.
Coleman, Sidney (1988), Aspects of Symmetry, Cambridge University Press.
Coqblin, B. (1977), Electronic Structure of Rare-Earth Metals and Alloys: the Magnetic Heavy Rare-Earths, London: Academic Press Inc.
Combescot, R. and Mora, C. (2005), Eur. Phys. J. B44, 189.
Continentino, M. A. and Rivier, N. (1977), J. Phys. C: Solid State Physics 10, 3613.
Continentino, M. A., Japiassu, G. and Troper, A. (1989) Phys. Rev. B39, 9734.
Continentino, M. A. (1991a), J. de Physique I 1, 693.
Continentino, M. A. (1991b), Phys. Rev. B43, 6292.
Continentino, M. A. (1993), Phys. Rev. B47, 11587.
Continentino, M. A. (1994a), Phys. Rep., 239, 179.
Continentino, M. A. and Coutinho-Filho, M. D. (1994b), Sol. St. Comm. 90, 619.
Continentino, M. A. (1995a), Phys. Lett. A 197, 417.
Continentino, M. A., Elschner, B. and Jakob, G. (1995b), Europhys. Lett. 31, 485.
Continentino, M. A. (1996), Zeitschrift für Physik B101, 197.
Continentino, M. A. (1998), Phys. Rev. B57, 5966.
Continentino, M. A. (2000), Eur. Phys. J. B13, 31.
Continentino, M. A. and Ferreira, A. S. (2004), PHYSICA A 339, 461.
Continentino, M. A. and Ferreira, A. S. (2007), JMMM, 310, 828.
Continentino, M. A. (2011), Braz. J. Phys. 41, 201.
Continentino, M. A., Deus, F. and Caldas, H. (2014) Phys. Lett. A 378, 1561.
Continentino, M. A., Caldas, H., Nozadze, D., Trivedi, N. (2014), Phys. Lett. A378, 3340.
DeGottardi, W., Sen, Diptiman and Vishveshwara, S. (2011), New Journal of Physics 13, 065028.
de Mello, E. V and Continentino, M. A. (1990), J.Phys. Condensed Matter 2, 4161.
Deus, Fernanda and Continentino, Mucio (2013), Philo. Mag. 93, 3062.
Dolan, L. and Jackiw, R. (1974), Phys. Rev. D9, 3320.
Doniach, S. (1977), Physica B91, 231; dos <Santos, R. R. (1982), J. Phys. C: Solid State Phys. 5, 3141.
Enderlein, C., Ramos, S. M., Bittencourt, M., Continentino, M. A., Brewer, W. and Baggio-Saitovich, E. (2013), J. Appl. Phys. 114, 143711.
Enderlein, C., Fontes, M., Baggio-Saitovitch, E. and Continentino, M. A. (2016), Journal of Magnetism and Magnetic Materials 398, 270.
Ferreira, A. S., Continentino, M. A. and Marino, E. C. (2004), Phys. Rev. B70, 174507.
Fisher, M. E. and Berker, A. N. (1982), Phys. Rev. B26, 2507.
Fisher, M. E. (1983), in Critical Phenomena, ed. by Hahne, F. J. W. (ed.) Berlin: Springer Verlag, 1.
Fisher, M. P. A., Weichman, P. B., Grinstein, G. and Fisher, D. S. (1989), Phys. Rev. B40, 546.
Fisher, M. P. A., Grinstein, G. and Girwin, S. (1990) Phys. Rev. Lett. 64, 587.
Kambe, S., Flouquet, J. and Hargreaves, T. E. (1997), J. Low Temp. Phys. 108, 383.
Foo, E-Ni and Giangiulio, D. J. (1976), PHYSICA 84B, 167.
Fradkin, E. (1991), Field Theories of Condensed Matter Systems, Redwood City, CA: Addison-Wesley.
Freitas, D. C., Rodière, P., Núñez, M., Garbarino, G., Sulpice, A., Marcus, J., Gay, F., Continentino, M. A. and Núñez-Regueiro, M. (2015), Phys. Rev. B 92, 205123.
Fulde, P. and Ferrell, R.A. (1964), Phys. Rev. A135, 550.
Georges, A., Kotliar, G., Krauth, W. and Rozenberg, M. J. (1996), Rev. Mod. Phys. 68, 73.
Georges, A., Kotliar, G., Krauth, W. and Rozenberg, M. J. (1996), Rev. Mod. Phys. 68, 13.
Goldenfeld, N. (1992), Lectures on Phase Transitions and the Renormalization Group, USA: Addison-Wesley Publishing Company.
Gorkov, L. P. and Melik-Barkhudarov, T. K. (1961), Zh. Eksp. Teor. Fiz. 40, 1452; (1961), Sov. Phys. JETP 13, 1018).
Granato, E. and Continentino, M. A. (1993), Phys. Rev. B, 15977.
Gutzwiller, M. C. (1965), Phys. Rev. A137, A1726.
Halperin, B. I. and Rice, T. M. (1968), Rev. Mod. Phys. 40, 755.
Halperin, B. I., Lubensky, T. and Ma, S.-K. (1974), Phys. Rev. Lett. 32, 292.
Harper, P. G. (1955), Proc. Phys. Soc. Lond. Sect. A68, 874.
Hasan, M. Z. and Kane, C. L. (2010) Rev. Mod. Phys. 82, 3045.
Hayden, S. M. et al. (2000), Phys. Rev. Lett. 84, 999.
Hertz, J. A. (1976), Phys. Rev. B14, 1165.
Hiramoto, H. and Kohmoto, M. (1989), Phys. Rev. B 40, 8225.
Hofstadter, D. R. (1976), Phys. Rev. B14, 2239.
Huang, K. (2015), in Ken Wilson Memorial Volume: Renormalization, Lattice Gauge Theory, the Operator Product Expansion and Quantum Fields, Baaquie, B. E., Huang, K., Peskin, M. E. and Phua, K. K. (eds.), World Scientific, 19.
Hubbard, J. (1963), Proc. Roy. Soc. London Ser. A276, 238.
Hubbard, J. (1964a), Proc. Roy. Soc. London Ser. A277, 237.
Hubbard, J. (1964b), Proc. Roy. Soc. London Ser. A281, 401.
Imada, M., Fujimori, A. and Tokura, Y. (1998), Rev. Mod. Phys. 70, 1039.
Ingold, G-L., Wobst, A., Aulbach, C. and Hanggi, P. (2002), Eur. Phys. J. B30, 175.
Jaccard, D., Behnia, K. and Sierro, J. (1992), Phys. Lett. A 163, 475.
Jackiw, R. (1973), Phys. Rev. D9, 1686.
Jullien, R. (1981), Can. J. Phys. 59, 605.
Kadanoff, L. P., Gotze, W., Hamblen, D. et al. (1967), Rev. Mod. Phys. 39, 395.
Kadowaki, K. and Woods, S. B. (1986), Solid St. Comm. 58, 507.
Kaganov, M. I. and Möbius A. (1984), Sov. Phys. JETP 59, 405.
Kanamori, J. (1963), Prog. Theor. Phys. 30, 275.
Kawakami, N. and Yang, S.-K. (1990), Phys. Rev. Lett. 65, 3063.
Kehrein, Stefan (2006) in The Flow Equation Approach to Many-Particle Systems, Springer Tracts in Modern Physics Volume 217, Berlin Heidelberg: Springer-Verlag.
Kitaev, A. Y. (2001), Physics-Uspekhi 44, 131.
Kitaev, A. Y. (2003), Annals of Physics 303, 2.
Kleinert, H. (1987), Gauge Fields in Condensed Matter/Volume 1: Superflow and Vortex Lines/Volume 2: Stresses and Defects, World Scientific Publishing Company, Incorporated.
Kohmoto, M. (1983), Phys. Rev. Lett 51, 1198.
Kohn, W. (1964), Phys. Rev. A133, 171.
Kotliar, G. and Ruckenstein, A. (1986), Phys. Rev. Lett. 57, 11.
Lacroix, C. and Pinettes, C. (1995), Physica B 206&207, 11.
Landau, L. D. and Lifshitz, E. M. (1980), Statistical Mechanics, Oxford: Pergamon Press.
Larkin, A. I. and Ovchinnikov, Yu. N. (1965) Sov. Phys. JETP 20, 762.
Lavagna, M. (1990), Phys. Rev. B41, 142.
Lederer, P. and Mills, D. L.(1968), Phys. Rev. 165, 837.
Lee, P. A. and Ramakrishnan, T. V. (1985), Rev. Mod. Phys. 57, 287.
Linde, A. D. (1979), Rep. Prog. Phys. 42, 389.
Löhneysen, v. H. et al. (1994), Phys. Rev. Lett. 72, 3262.
Loram, J. W., Mirza, K. A. and Freeman, P. F. (1990) Physica C 171, 243.
Luengo, C. A., Maple, M. B. and Fertig, W. A. (1972) Solid State Commun. 11, 1445.
Ma, S.-K. (1976), Modern Theory of Critical Phenomena, Reading, MA: Addison-Wesley.
Malbuisson, A. P. C., Nogueira, F. S. and Svaiter, N. F. (1996), Mod. Phys. Lett. 11, 749.
Mathur, N. D., Grosche, F. M., Julian, S. R., Walker, I. R., Freye, D. M., Haselwimmer, R. K. W. and Lonzarich, G. G. (1998), Nature 394, 39.
Medeiros, S. N. et al. (2000), Physica B281&282, 340.
Millis, A. J., Monien, H. and Pines, D. (1990), Phys. Rev. B 42, 167.
Millis, A. J. (1993), Phys. Rev. B48, 7183.
Mineev, V. P. and Sigrist, M. (2001), Phys. Rev. B63, 172504.
Mineev, V. P. and Zhitomirsky, M. E. (2005) Phys. Rev. B72, 014432.
Miranda, E., Dobrosavljevic, V. and Kotliar, G. (1996), Phys.Rev.Lett. 78, 290;
Miranda, E., García, D. J., Hallberg, K. and Rozenberg, M. J. (2008), Physica B 403, 1465.
Mitra, A. (2008), Phys. Rev. B78, 214512.
Moriya, T. (1985) Spin Fluctuations in Itinerant Electron Magnetism, Berlin Heidelberg: Springer-Verlag.
Moriya, T. and Takimoto, T. (1995), J. Phys. Soc. Jpn. 64, 960.
Mott, N. F. (1974), Metal-Insulator Transitions, London: Taylor and Francis.
Murakami, Shuichi (2007), New Journal of Physics 9, 356.
Negele, J. W. and Orland, H. (1988), Quantum Many-Particle Systems, Redwood City, CA: Addison-Wesley.
Nienhuis, B. and Naunberg, M. (1975), Phys. Rev. Lett. 35, 477.
Nogueira, F. S. (1996), PhD. Thesis, Centro Brasileiro de Pesquisas Fisicas, unpublished.
Nozadze, D. and Trivedi, N. (2016) Phys. Rev. B93, 064512.
Nozières, P. (1986), Magnétisme et Localization dans les Liquides de Fermi, Collège de France, unpublished.
Oliveira, P. M., Continentino, M. A. and Anda, E. (1984), Phys. Rev. B29, 2808.
Padilha, Igor, T. and Continentino, M. A. (2009), Physica B – Condensed Matter, 404, 2920.
Peskin, M. E. and Schroeder, D. V. (1995), An Introduction to Quantum Field Theory, First Edition, Frontiers in Physics, Westview Press.
Pfeuty, P. (1970), Ann. Phys. 57, 79.
Pfeuty, P., Jullien, R. and Penson, K. A. (1982), Real Space Renormalisation Group, Berlin: Springer Verlag, 119.
Pfeuty, P., Jasnow, D. and Fisher, M. E. (1974), Phys. Rev. B10, 2088.
Prokovsky, V. L. and Tapalov, A. L. (1979), Phys. Rev. Lett. 41, 65.
Puel, T. O., Sacramento, P. D. and Continentino, M. A. (2015), J. of Phys. – Cond. Mat. 27, 422002.
Ramazashvili, R. (1999), Phys. Rev. B60, 7314.
Ramazashvili, R. and Coleman, P. (1997), Phys.Rev.Lett. 79, 3752.
Ramires, A. and Continentino, M. A. (2010), J. Phys.: Condens. Matter 22, 485701.
Rezende, S. M. (1975) in Brazilian Symposium on Theoretical Physics, Livros Técnicos e Científicos Editora S.A., edited by Erasmo, Ferreira and Rio de Janeiro, RJ, Vol. 2, 3; Rezende, S. M., King, A. R., White, R. M. and Timbie, J. P.(1977), Phys. Rev. B16, 1126.
Ribeiro, F. G., de Lima, J. P. and Gonçalves, L. L. (2011), JMMM 323, 39.
Rosch, A., Schröder, A. Stockert, O. and Löhneysen, H. (1997), Phys.Rev.Lett. 79, 159.
Sachdev, S, (1996), Proceedings of the 19th IUPAP International Conference on Statistical Mechanics, Singapore: World Scientific.
Sachdev, S. (1999), Quantum Phase Transitions, Cambridge University Press.
Sachdev, S., Read, N. and Oppermann, R. (1995), Phys. Rev. B52, 10286.
Sachdev, S. (1994), Z. Phys. B94, 469.
Sachdev, S. (2011), Quantum Phase Transitions, Second Edition, Cambridge University Press.
Samokhin, K. V. and Marénko, M. S. (2006), Phys. Rev. B73, 144502.
Scalapino, D. J., White, S. R. and Zhang, S. C. (1992), Phys. Rev. Lett. 68, 2830.
Scalapino, D. J., White, S. R. and Zhang, S. C. (1993), Phys. Rev. B 47, 7995.
Schröder, A., Aeppli, G., Bucher, E. et al. (1998), Phys. Rev. Lett. 80, 5623.
Schuberth, E., Tippmann, M., Steinke, L., Lausberg, S., Steppke, A., Brando, M., Krellner, C., Geibel, C., Yu, Rong, Si, Qimiao, Steglich and F. (2106), SCIENCE 351, 485.
Shastry, B. and Sutherland, B. (1990), Phys. Rev. Lett. 65, 243.
Shimahara, Hiroshi (1994), Phys. Rev. B50, 12760.
Shimahara, Hiroshi (1998), J. Phys. Soc. Jpn. 67, 736.
Shockley, W. (1939) Phys. Rev. 56, 317.
Sólyom, J. (1987), Phys. Rev. B36, 8642
Sondhi, S. L. et al. (1997), Rev. Mod. Phys. 69, 315.
Stanley, H. E. (1971), Introduction to Phase Transitions and Critical Phenomena, Oxford University Press.
Steglich, F., Geibel, C., Helfrisch, R. et al. (1998), J. Phys. Chem. Solids 59, 2190.
Steglich, F., Geibel, C., Modler, R. et al. (1995), J. Low Temp. Phys. 99, 267.
Strogatz, S. (2014), Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), Second Edition, USA: Westview Press.
Suhl, H., Matthias, B. T. and Walker, L. R. (1959), Phys.Rev.Lett. 3, 552.
Takimoto, T. and Moriya, T. (1996), Solid State Comm. 99, 457.
Thompson, J. D. and Lawrence, J. M. (1994), Handbook on the Physics and Chemistry of Rare Earths, Lanthanides/Actinides: Physics-II, K. A., Gschneider Jr., L., Eyring, G. H., Lander and G. R., Choppin (eds), Elsevier Science B.V., Chapter 133 (19), 383.
Thouless, D. J. (1960), Ann. Phys. 10, 553.
Toulouse, G. (1974), Nuovo Cimento B23, 234.
Toulouse, G. and Pfeuty, P (1975), Introduction au Groupe de Renormalisation et à ses Applications, Presses Universitaires de Grenoble.
Tyablikov, S. V. (1967) Methods in the Quantum Theory of Magnetism, New York, NY: Plenum Press.
Vitoriano, C., Bejan, L. B., Macedo, A. M. S. and Coutinho-Filho, M. D. (2000), Phys. Rev. 61, 7941.
Vollhardt, D. (1984), Rev. Mod. Phys. 56, 99.
Vollhardt, D. (2012), Ann. Phys. (Berlin) 524, 1.
Volovik, G. E. (2009), The Universe in a Helium Droplet, New York, NY: Oxford University Press.
Vučičević, J., Tanasković, D., Rozenberg, M. J. and Dobrosavljević, V. (2015), Phys.Rev.Lett. 114, 246402.
Wilson, K. G. (1971), Phys. Rev. B4, 3174.
Wilson, K. G. (1975), Rev. Mod. Phys. 47, 1773.
White, S. R. (1992), Phys. Rev. Lett. 69, 2863.
White, S. R. (1993), Phys. Rev. B 48, 10345.
Young, A. P. (1975), J. Phys. C: Solid State Phys. 8, L309.
Yu, Rong, Miclea, Corneliu, F., Weickert, F., Movshovich, R., Paduan-Filho, A., Zapf, V. S. and Roscilde, T. (2012) Phys. Rev. B86, 134421.


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.