Pseudospin SU(2)-symmetry breaking, charge-density waves and superconductivity in the Hubbard model

Journal of Physics Condensed Matter

Volumn 8, Issue 26, 1996, Pages 4805-4812

  Shen, Shun Qing ^a,b   Xie, X C ^a  

^a OKLAHOMA STATE UNIVERSITY   (United States)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; CHARGED PARTICLES; ELECTRON ENERGY LEVELS; MAGNETIC FIELDS; MATHEMATICAL MODELS; SUPERCONDUCTIVITY;

CHARGE DENSITY WAVES; HUBBARD MODEL; PSEUDOSPIN SYMMETRY BREAKING;

QUANTUM THEORY;

EID: 0030170269     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/8/26/012     Document Type: Article

References (43)

1. For example, see, Anderson P W 1983 Basic Notations of Condensed Matter Physics (New York: Benjamin)
2. Jones B A, Varma C M and Wilkins J W 1988 Phys. Rev. Lett. 61 125
3. Yang C N 1989 Phys. Rev. Lett. 62 2144
4. Yang C N and Zhang S C 1990 Mod. Phys. Lett. 34 759 Yang C N 1991 Phys. Lett. 161A 292
5. Yang C N and Zhang S C 1990 Mod. Phys. Lett. 34 759 Yang C N 1991 Phys. Lett. 161A 292
6. Zhang S C 1990 Phys. Rev. Lett. 65 120; 1991 Strongly Correlated Electron Systems II ed G Baskaran et al (Singapore: World Scientific) p 153
7. Zhang S C 1990 Phys. Rev. Lett. 65 120; 1991 Strongly Correlated Electron Systems II ed G Baskaran et al (Singapore: World Scientific) p 153
8. Shen S-Q and Qiu Z-M 1993 Phys. Rev. Lett. 71 4238
9. Pu F-C and Shen S-Q 1994 Phys. Rev. B 50 16086
10. Singh R R P and Scalettar R T 1991 Phys. Rev. Lett. 66 3203 Rojo A G, Sofo J O and Balseiro C A 1990 Phys. Rev. B 42 10241 Sofo J O and Balseiro C A 1992 Phys. Rev. Lett. 68 896
11. Singh R R P and Scalettar R T 1991 Phys. Rev. Lett. 66 3203 Rojo A G, Sofo J O and Balseiro C A 1990 Phys. Rev. B 42 10241 Sofo J O and Balseiro C A 1992 Phys. Rev. Lett. 68 896
12. Singh R R P and Scalettar R T 1991 Phys. Rev. Lett. 66 3203 Rojo A G, Sofo J O and Balseiro C A 1990 Phys. Rev. B 42 10241 Sofo J O and Balseiro C A 1992 Phys. Rev. Lett. 68 896
13. Shiba H 1972 Prog. Theor. Phys. 48 2171 Nagaoka Y 1974 Prog. Theor. Phys. 52 1716 Emery V J 1972 Phys. Rev. B 14 2989 Robaszkiewicz S, Micnac R and Chao K A 1981 Phys. Rev. B 23 1447
14. Shiba H 1972 Prog. Theor. Phys. 48 2171 Nagaoka Y 1974 Prog. Theor. Phys. 52 1716 Emery V J 1972 Phys. Rev. B 14 2989 Robaszkiewicz S, Micnac R and Chao K A 1981 Phys. Rev. B 23 1447
15. Shiba H 1972 Prog. Theor. Phys. 48 2171 Nagaoka Y 1974 Prog. Theor. Phys. 52 1716 Emery V J 1972 Phys. Rev. B 14 2989 Robaszkiewicz S, Micnac R and Chao K A 1981 Phys. Rev. B 23 1447
16. Shiba H 1972 Prog. Theor. Phys. 48 2171 Nagaoka Y 1974 Prog. Theor. Phys. 52 1716 Emery V J 1972 Phys. Rev. B 14 2989 Robaszkiewicz S, Micnac R and Chao K A 1981 Phys. Rev. B 23 1447
17. Micnas R, Ranninger J and Robaszkiewicz S 1991 Rev. Mod. Phys. 62 3203 and references therein
18. Soni V and Thakur J S 1993 Phys. Rev. B 48 12917
19. 2) [4]. In the negative-U case, it was shown that the spin SU(2) symmetry could not be spontaneously broken [13]. Thus we will not consider the spin SU(2) symmetry in this paper. By the term SU(2) symmetry, (if used without any qualification) we will always mean pseudospin symmetry in this paper.
20. Kubo K and Kishi T 1990 Phys. Rev. B 41 4866
21. Goldstone J 1960 Nuovo Cimento 19 154 Nambu Y and Jona-Lasinio G 1961 Phys. Rev. 122 345; 1961 Phys. Rev. 124 246 Goldstone J, Salam A and Weinberg S 1962 Phys. Rev. 127 965
22. Goldstone J 1960 Nuovo Cimento 19 154 Nambu Y and Jona-Lasinio G 1961 Phys. Rev. 122 345; 1961 Phys. Rev. 124 246 Goldstone J, Salam A and Weinberg S 1962 Phys. Rev. 127 965
23. Goldstone J 1960 Nuovo Cimento 19 154 Nambu Y and Jona-Lasinio G 1961 Phys. Rev. 122 345; 1961 Phys. Rev. 124 246 Goldstone J, Salam A and Weinberg S 1962 Phys. Rev. 127 965
24. Goldstone J 1960 Nuovo Cimento 19 154 Nambu Y and Jona-Lasinio G 1961 Phys. Rev. 122 345; 1961 Phys. Rev. 124 246 Goldstone J, Salam A and Weinberg S 1962 Phys. Rev. 127 965
25. Heeger A J, Kivelson S, Schrieffer J R and Su W-P 1988 Rev. Mod. Phys. 60 781
26. Bardeen J, Cooper L N and Schrieffer J R 1957 Phys. Rev. 108 1175
27. This inequality can be proven by using the spin-reflection positivity in the ground state of a negalive-U Hubbard model. The proof can be seen in [6, 18]. In the former, we proved the equality part of the inequality; in the latter we proved a similar spin-operator inequality for a positive-U Hubbard model at half-filling, and this inequality for pseudospin operators can easily be obtained by using the partial particle-hole transformation from the positive-U case.
28. Shen S-Q, Qiu Z-M and Tian G-S 1994 Phys. Rev. Lett. 72 1280
29. Schrieffer J R 1964 Theory of Superconductivity (Reading, MA: Addison-Wesley)
30. Lieb E 1990 Phys. Rev. Lett. 62 1201
31. Scalapino D J, White S R and Zhang S C 1992 Phys. Rev. Lett. 68 2830; 1993 Phys. Rev. B 47 7995
32. Scalapino D J, White S R and Zhang S C 1992 Phys. Rev. Lett. 68 2830; 1993 Phys. Rev. B 47 7995
33. The superfluid density defined here is related to the penetration depth of an external magnetic field. When it is not equal to zero, the penetration depth is finite and the state is diamagnetic. Usually the CDW states are insulating and the Drude weight should be zero (or the resistance is equal to zero) In this case the quasiparticle spectrum has a gap, and the superfluid density is equal to the Drude weight [21], i.e., the superfluid density in an insulating CDW state is always zero.
34. Tian G S 1994 Phys. Lett. 192A 278
35. Smith T F, Shelton R N and Schwall R E 1974 J. Phys. F: Met. Phys. 4 2009 Wilson A J, Di Salvo F J and Mahajan S 1975 Adv. Phys. 24 117 Berthier C, Molinie P and Jerome D 1976 Solid State Commun. 18 1393
36. Smith T F, Shelton R N and Schwall R E 1974 J. Phys. F: Met. Phys. 4 2009 Wilson A J, Di Salvo F J and Mahajan S 1975 Adv. Phys. 24 117 Berthier C, Molinie P and Jerome D 1976 Solid State Commun. 18 1393
37. Smith T F, Shelton R N and Schwall R E 1974 J. Phys. F: Met. Phys. 4 2009 Wilson A J, Di Salvo F J and Mahajan S 1975 Adv. Phys. 24 117 Berthier C, Molinie P and Jerome D 1976 Solid State Commun. 18 1393
38. Lee P A, Rice T M and Anderson P W 1974 Solid State Commun. 14 703 Balseiro C A and Falicov L M 1980 Phys. Rev. Lett. 45 662 Littlewood P B and Varma C M 1981 Phys. Rev. Lett. 47 811; 1982 Phys. Rev. B 26 4883
39. Lee P A, Rice T M and Anderson P W 1974 Solid State Commun. 14 703 Balseiro C A and Falicov L M 1980 Phys. Rev. Lett. 45 662 Littlewood P B and Varma C M 1981 Phys. Rev. Lett. 47 811; 1982 Phys. Rev. B 26 4883
40. Lee P A, Rice T M and Anderson P W 1974 Solid State Commun. 14 703 Balseiro C A and Falicov L M 1980 Phys. Rev. Lett. 45 662 Littlewood P B and Varma C M 1981 Phys. Rev. Lett. 47 811; 1982 Phys. Rev. B 26 4883
41. Lee P A, Rice T M and Anderson P W 1974 Solid State Commun. 14 703 Balseiro C A and Falicov L M 1980 Phys. Rev. Lett. 45 662 Littlewood P B and Varma C M 1981 Phys. Rev. Lett. 47 811; 1982 Phys. Rev. B 26 4883
42. Sooryakumar R and Klein M V 1980 Phys. Rev. Lett. 45 660 Sooryakumar R, Klein M V and Frindt R F 1981 Phys. Rev. B 23 3222
43. Sooryakumar R and Klein M V 1980 Phys. Rev. Lett. 45 660 Sooryakumar R, Klein M V and Frindt R F 1981 Phys. Rev. B 23 3222