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Integrable extended Hubbard models with boundary Kondo impurities

Published online by Cambridge University Press:  17 April 2009

Anthony J. Bracken ,
Xiang-Yu Ge ,
Mark D. Gould  and
Huan-Qiang Zhou
Anthony J. Bracken
Affiliation:
Centre for Mathematical Physics, The University of Queensland, Brisbane, Qld 4072, Australia e-mail: xg@maths.uq.edu.au
Xiang-Yu Ge
Affiliation:
Centre for Mathematical Physics, The University of Queensland, Brisbane, Qld 4072, Australia e-mail: xg@maths.uq.edu.au
Mark D. Gould
Affiliation:
Centre for Mathematical Physics, The University of Queensland, Brisbane, Qld 4072, Australia e-mail: xg@maths.uq.edu.au
Huan-Qiang Zhou
Affiliation:
Centre for Mathematical Physics, The University of Queensland, Brisbane, Qld 4072, Australia e-mail: xg@maths.uq.edu.au
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Abstract

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Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 445 - 467
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Anderson, P.W., ‘The resonating valence bond state in La2CuO4 and superconductivity’, Science 235 (1987), 1196–1198.CrossRefGoogle Scholar
[2]Bracken, A.J., Ge, X.-Y., Zhang, Y.-Z. and Zhou, H.-Q., ‘Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons’, Nuclear Phys. B 516 (1998), 588–602.CrossRefGoogle Scholar
[3]Essler, F.H.L. and Korepin, V.E., ‘Higher conservation laws and algebraic Bethe ansatz for the supersymmetric t – J model’, Phys. Rev. B 46 (1992), 9147–9162.CrossRefGoogle Scholar
[4]Essler, F.H.L. and Korepin, V.E., ‘Spectrum of low-lying excitations in a supersymmetric extended Hubbard model’, Internat. J. Modern. Phys. B 8 (1994), 3243–3279.Google Scholar
[5]Essler, F.H.L., Korepin, V.E. and Schoutens, K., ’New exactly solvable model of strongly correlated electrons motivated by high T c superconductivity’, Phys. Rev. Lett. 68 (1992), 2960–2963.Google Scholar
[6]Essler, F.H.L., Korepin, V.E. and Schoutens, K., ‘Electronic model for superconductivity’, Phys. Rev. Lett. 70 (1993), 73–76.Google Scholar
[7]Essler, F.H.L., Korepin, V.E. and Schoutens, K., ‘Exactly solution of an electronic model of superconductivity’, Internat. J. Modern. Phys. A 8 (1994), 3205–3242.Google Scholar
[8]Fan, H., Wadati, M. and Yue, R.-H., ‘Boundary impurities in the generalized supersymmetric t – J model’, J. Phys. A 33 (2000), 6187–6202.CrossRefGoogle Scholar
[9]Frahm, H. and Slavnov, N.A., ‘New solution of the reflection equation and the projecting method’, J. Phys. A 32 (1999), 1547–1555.CrossRefGoogle Scholar
[10]Ge, X.-Y., ‘Integrable open-boundary conditions for the q-deformed extended Hubbard model’, Modern. Phys. Lett. B 13 (1999), 499–507.Google Scholar
[11]Ge, X.-Y., Gould, M.D., Links, J. and Zhou, H.-Q., ‘Integrable Kondo impurity in one-dimensional q-deformed t – J models’, J. Phys. A (to appear).Google Scholar
[12]Hu, Z.-N., Pu, F.-C. and Wang, Y., ‘Integrability of the t – J model with impurities’, J. Phys. A 31 (1998), 5241–5262.Google Scholar
[13]Schlottmann, P. and Zvyagin, A.A., ‘Kondo impurity band in a one-dimensional correlated electron lattice, Phys. Rev. B 56 (1997), 13989–13998.Google Scholar
[14]Schoutens, K., ‘Complete solution of a supersymmetric extended Hubbard model’, Nuclear Phys. B 413 (1994), 675–688.Google Scholar
[15]Shastry, B.S., ‘Exact integrability of the one-dimensional Hubbard model’, Phys. Rev. Lett. 56 (1986), 2453–2455.Google Scholar
[16]Shastry, B.S., ‘Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model’, J. Statist. Phys. 50 (1988), 57–79.CrossRefGoogle Scholar
[17]Sklyanin, E.K., ‘Boundary conditions for integrable quantum systems’, J. Phys. A 21 (1988), 2375–2389.Google Scholar
[18]Sklyanin, E.K., Takhtajan, L.A. and Faddeev, L.D., ‘Quantum inverse problem method I’, Theoret. and Math. Phys. 40 (1980), 688–706.CrossRefGoogle Scholar
[19]Wang, Y., Dai, J.-H., Hu, Z.-N. and Pu, F.-C., ‘Exact results for a Kondo problem in one dimensional t – J model’, Phys. Rev. Lett. 79 (1997), 1901–1904.Google Scholar
[20]Zhang, F.C. and Rice, T.M., ‘Effective Hamiltonian for the superconducting Cu oxides’, Phys. Rev. B 37 (1988), 3759–3761.Google Scholar
[21]Zhou, H.-Q., Ge, X.-Y. and Gould, M.D., ‘Integrable Kondo impurities in the one-dimensional supersymmetric extened Hubbard model’, J. Phys. A 32 (1999), 5383–5388.Google Scholar
[22]Zhou, H.-Q., Ge, X.-Y., Links, J. and Gould, M.D., ‘Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t – J model’, Nuclear. Phys. B 546 (1999), 779–799.Google Scholar
[23]Zhou, H.-Q., Ge, X.-Y., Links, J. and Gould, M.D., ‘Integrable Kondo impurities in the one-dimensional extended Hubbard models’, Phys. Rev. B 62 (2000), 4906–4921.Google Scholar
[24]Zhou, H.-Q. and Gould, M.D., ‘Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t – J model’, Phys. Lett. A 251 (1999), 279–285.CrossRefGoogle Scholar
[25]Zvyagin, A.A. and Schlottmann, P., ‘Exact solution for a one-dimensional multichannel model of correlated electrons with an Anderson-like impurity’, J. Phys. A 31 (1998), 1981–1987.Google Scholar