Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice

European Physical Journal B

Volumn 38, Issue 3, 2004, Pages 409-430

  Zhang, N G ^a,b   Henley, C L ^a  

^a Cornell University   (United States)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; CRYSTAL LATTICES; FERMI LIQUIDS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING;

ANYON MECHANISMS; BOSON SYSTEMS; LUTTINGER LIQUIDS; VALENCE BONDS;

FERMIONS;

EID: 3042572336     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2004-00135-8     Document Type: Article

References (72)

1. E. Dagotto, Rev. Mod. Phys. 66, 763 (1994)
2. E. Manousakis, Rev. Mod. Phys. 63, 1 (1991)
3. E.H. Lieb, D.C. Mattis, Mathematical Physics in One Dimension (Academic, New York, 1966)
4. S.R. White, Phys. Rev. Lett. 69, 2863 (1992); S.R. White, D.J. Scalapino, Phys. Rev. Lett. 80, 1272 (1998)
5. S.R. White, Phys. Rev. Lett. 69, 2863 (1992); S.R. White, D.J. Scalapino, Phys. Rev. Lett. 80, 1272 (1998)
6. Y. Nagaoka, Phys. Rev. 147, 392 (1966)
7. R.J. Bursill, Phys. Rev. B 60, 1643 (1999); C.J. Bolech, S.S. Kancharla, G. Kotliar, Phys. Rev. B 67, 075110 (2003)
8. R.J. Bursill, Phys. Rev. B 60, 1643 (1999); C.J. Bolech, S.S. Kancharla, G. Kotliar, Phys. Rev. B 67, 075110 (2003)
9. H.Q. Lin, J.E. Gubernatis, Comp. Phys. 7, 400 (1993)
10. G. Fano, F. Ortolani, A. Parola, Phys. Rev. B 46, 1048 (1992)
11. H. Bruus, J.-C. Angles d'Auriac, Phys. Rev. B 55, 9142 (1997)
12. M. Schick, Phys. Rev. A 3, 1067 (1971)
13. F. Becca, L. Capriotti, S. Sorella, A. Parola, Phys. Rev. B 62, 15277 (2000)
14. G. Batrouni (private communication); K. Bernardet, G.G. Batrouni, J.-L. Meunier, G. Schmid, M. Troyer, A. Dorneich, Phys. Rev. B 65, 104519 (2002)
15. G. Batrouni (private communication); K. Bernardet, G.G. Batrouni, J.-L. Meunier, G. Schmid, M. Troyer, A. Dorneich, Phys. Rev. B 65, 104519 (2002)
16. Our exact diagonalization computer program can handle arbitary periodic boundaries specified by two vectors on the square lattice and uses translation symmetry to reduce the matrix size. It is described in references [14, 15]
17. N.G. Zhang, C.L. Henley, Phys. Rev. B 68, 014506 (2003)
18. N.G. Zhang, Ph.D. thesis, Cornell University (2002)
19. G. Zala, B.N. Narozhny, I.L. Aleiner, V.I. Falko, Phys. Rev. B 69, 075306 (2004)
20. D. Vollhardt, in Proceedings of the Enrico Fermi School, Course CXXI, edited by Broglia, Schrieffer (North-Holland, Amsterdam, 1994)
21. C.N. Yang, C.P. Yang, Phys. Rev. 150, 321 and 327 (1966)
22. G.S. Uhrig, R. Vlaming, Phys. Rev. Lett. 71, 271 (1993); G.S. Uhrig, R. Vlaming, Physica B 194-196, 451 (1994); G.S. Uhrig, R. Vlaming, Physica B 206-207, 694 (1995), G.S. Uhrig, R. Vlaming, Ann. Physik 4, 778 (1995)
23. G.S. Uhrig, R. Vlaming, Phys. Rev. Lett. 71, 271 (1993); G.S. Uhrig, R. Vlaming, Physica B 194-196, 451 (1994); G.S. Uhrig, R. Vlaming, Physica B 206-207, 694 (1995), G.S. Uhrig, R. Vlaming, Ann. Physik 4, 778 (1995)
24. G.S. Uhrig, R. Vlaming, Phys. Rev. Lett. 71, 271 (1993); G.S. Uhrig, R. Vlaming, Physica B 194-196, 451 (1994); G.S. Uhrig, R. Vlaming, Physica B 206-207, 694 (1995), G.S. Uhrig, R. Vlaming, Ann. Physik 4, 778 (1995)
25. G.S. Uhrig, R. Vlaming, Phys. Rev. Lett. 71, 271 (1993); G.S. Uhrig, R. Vlaming, Physica B 194-196, 451 (1994); G.S. Uhrig, R. Vlaming, Physica B 206-207, 694 (1995), G.S. Uhrig, R. Vlaming, Ann. Physik 4, 778 (1995)
26. R. Shankar Rev. Mod. Phys. 66, 129 (1994)
27. J.E. Gubernatis, D.J. Scalapino, R.L. Sugar, W.D. Toussaint, Phys. Rev. B 32, 103 (1985)
28. J.-L. Pichard, G. Benenti, G. Katomeris, F. Selva, X. Waintal, Exotic States in Quantum Nanostructures, edited by S. Sarkar (Kluwer, Dordrecht, 2002). One could speculate that, if their model included our infinitely strong nearest-neighbor repulsion, the Hilbert space (identical to ours) would be substantially reduced, without very much error in the energies
29. C.L. Henley, N.G. Zhang, Phys. Rev. B 63, 233107 (2001)
30. Note that with spinless fermions and hardcore bosons and infinite nearest-neighbor repulsion, the filling (particle per lattice site) in our model goes from 0 to 1/2 only
31. D.C. Mattis, The Theory of Magnetism, Vol. I (Springer, Berlin, 1981), p. 252
32. G. Baym, Lectures on Quantum Mechanics, Chap. 8, Cooper Pairs (Benjamin-Cummings, Reading, 1981)
33. S.-J. Dong, C.N. Yang, Rev. Math. Phys. 1, 139 (1989)
34. F. Marsiglio, J.E. Hirsch, Physica C 171, 554 (1990)
35. H.Q. Lin, Phys. Rev. B 44, 4674 (1991)
36. A.G. Petukhov, J. Galan, J.A. Verges, Phys. Rev. B 46, 6212 (1992)
37. A.S. Blaer, H.C. Ren. O. Tchernyshyov, Phys. Rev. B 55, 6035 (1997)
38. S. Basu, R.J. Gooding, P.W. Leung. Phys. Rev. B 63, 100506 (2001)
39. M. Fabrizio, A. Parola, E. Tosatti, Phys. Rev. B 44, 1033 (1991)
40. We are slightly abusing the notation V. V(r) is the potential function for all space. V is the value of the potential at four points (V = V(r = (1,0)) for example). And V(k) the Fourier transform of V(r). We will differentiate these meanings by including explicitly the argument, r or k. Without argument, we then mean V = V(r = (1,0))
41. The following derivation is indebted to reference [31] which solved a similar problem
42. Incidentally the interesting problem of computing the resistance between two points on a lattice resistor network turns out to be an application of the lattice Green functions. See J. Cserti, Am. J. Phys. 68, 896 (2000)
43. S. Katsura. S. Inawashiro, J. Math. Phys. 12, 1622 (1971)
44. T. Morita, J. Math. Phys. 12, 1744 (1971)
45. L.D. Landau, E.M. Lifshitz, Statistical Physics Vol. I (Addison, Reading, 1969), p. 234
46. A.L. Fetter. J.D. Walecka, Quantum Theory of ManyParticle Systems (McGraw, New York, 1971)
47. P. Bloom, Phys. Rev. B 12, 125 (1975)
48. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)
49. K. Yosida, Theory of Magnetism (Springer, Berlin, 1998), p. 191
50. S. Rudin, B.C. Mattis, Phys. Lett. 110A, 273 (1985)
51. M. Randeria, J.-M. Duan, L.-Y. Shieh, Phys. Rev. B 41, 327 (1990)
52. J.R. Engelbrecht. M. Randeria. L. Zhang, Phys. Rev. B 45, 10135 (1992)
53. J.R. Engelbrecht, M. Randeria, Phys. Rev. B 45, 12419 (1992)
54. H. Fukuyama, O. Narikiyo, Y. Hasegawa, J. Phys. Soc. Jpn 60, 372 (1991); H. Fukuyama. O. Narikiyo, Y. Hasegawa, J. Phys. Soc. Jpn 60, 2013 (1991)
55. H. Fukuyama, O. Narikiyo, Y. Hasegawa, J. Phys. Soc. Jpn 60, 372 (1991); H. Fukuyama. O. Narikiyo, Y. Hasegawa, J. Phys. Soc. Jpn 60, 2013 (1991)
56. y cos q, also has this pair component exchange symmetry
57. N. Furukawa, M. Imada, J. Phys. Soc. Jpn 61, 3331 (1992); M. Guerrero, G. Ortiz, J.E. Gubernatis, Phys. Rev. B 62, 600 (2000)
58. N. Furukawa, M. Imada, J. Phys. Soc. Jpn 61, 3331 (1992); M. Guerrero, G. Ortiz, J.E. Gubernatis, Phys. Rev. B 62, 600 (2000)
59. V. Galitskii, Sov. Phys. JETP 7, 104 (1958)
60. S. Beliaev, Sov. Phys. JETP 7, 289 (1958)
61. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957); K. Huang, C.N. Yang, J.M. Luttinger, Phys. Rev. 105, 776 (1957); T.D. Lee, C.N. Yang, Phys. Rev. 105, 1119 (1957); T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135 (1957)
62. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957); K. Huang, C.N. Yang, J.M. Luttinger, Phys. Rev. 105, 776 (1957); T.D. Lee, C.N. Yang, Phys. Rev. 105, 1119 (1957); T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135 (1957)
63. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957); K. Huang, C.N. Yang, J.M. Luttinger, Phys. Rev. 105, 776 (1957); T.D. Lee, C.N. Yang, Phys. Rev. 105, 1119 (1957); T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135 (1957)
64. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957); K. Huang, C.N. Yang, J.M. Luttinger, Phys. Rev. 105, 776 (1957); T.D. Lee, C.N. Yang, Phys. Rev. 105, 1119 (1957); T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135 (1957)
65. L.W. Bruch, Physica 93A, 95 (1978)
66. D.F. Hines, N.E. Frankel, D.J. Mitchell, Phys. Lett. 68A, 12 (1978)
67. E.H. Lieb, J. Yngvason, J. Stat. Phys. 103, 509 (2001)
68. J.O. Andersen, Eur. Phys. J. B 28, 389 (2002)
69. L.W. Bruch, Physica 94A, 586 (1978); G.S. Atwal (personal communication) has also derived equation (5.5) for general s
70. L.W. Bruch, Physica 94A, 586 (1978); G.S. Atwal (personal communication) has also derived equation (5.5) for general s
71. Reference [58] discusses spin degeneracy, but does not contain a formula for p-wave terms
72. B.R. Holstein, Topics in Advanced Quantum Mechanics (Addision, Redwood, 1992), p. 74