Effective Hamiltonians and phase diagrams for tight-binding models

Journal of Statistical Physics

Volumn 96, Issue 3-4, 1999, Pages 545-611

  Datta, Nilanjana ^a   Fernández, Roberto ^b   Fröhlich, Jürg ^c  

^a EPFL   (Switzerland)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c ETH ZURICH   (Switzerland)

Author keywords

One band hubbard models; Perturbation expansions; Phase diagrams; Pirogov sinai theory; Three band hubbard models; Tight binding models

Indexed keywords

EID: 0033245977     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004594122474     Document Type: Article

References (50)

1. 1. C. Albanese, On the spectrum of the Heisenberg Hamiltonian, J. Stat. Phys. 55:297-309 (1989).
2. 2. C. Albanese, Unitary dressing transformations and exponential decay below threshold for quantum spin systems, Parts I and II, Commun. Math. Phys. 134:1-27 (1990).
3. 3. C. Albanese, Unitary dressing transformations and exponential decay below threshold for quantum spin systems, Parts III and IV, Commun. Math. Phys. 134:237-272 (1990).
4. 4. P. W. Anderson, New approach to the theory of superexchange interactions, Phys. Rev. 115:2-13 (1959).
5. 5. C. Borgs, R. Kotecký, and D. Ueltschi, Low temperature phase diagrams for quantum perturbations of classical spin systems, Commun. Math. Phys. 181:409-46 (1996).
6. 6. J. Bricmont and J. Slawny, First order phase transitions and perturbation theory, in Statistical Mechanics and Field Theory: Mathematical Aspects (Proceedings, Groningen, 1985), T. C. Dorlas, N. M. Hugenholtz, and M. Winnink, eds. (Springer-Verlag, Berlin/ Heidelberg/New York, 1986) (Lecture Notes in Physics, Vol. 257).
7. 7. J. Bricmont and J. Slawny, Phase transitions in systems with a finite number of dominant ground states, J. Stat. Phys. 54:89-161 (1989).
8. 8. L. N. Bulaevskii, Quasihomopolar electron levels in crystals and molecules, Zh. Eksp. Teor. Fiz. 51:230-40 (1966). [Sov. Phys. JETP 24:154-60 (1967)].
9. 8. L. N. Bulaevskii, Quasihomopolar electron levels in crystals and molecules, Zh. Eksp. Teor. Fiz. 51:230-40 (1966). [Sov. Phys. JETP 24:154-60 (1967)].
10. 9. K. A. Chao, J. Spałek, and A. M. Oleś, Kinetic exchange interaction in a narrow S-band, J. Phys. C 10:L271-6 (1977).
11. 10. K. A. Chao, J. Spałek, and A. M. Oleś, Canonical perturbation expansion of the Hubbard model, Phys. Rev. B 18:3453-64 (1978).
12. 11. N. Datta, R. Fernández, and J. Fröhlich, Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states, J. Stat. Phys. 84:455-534 (1996).
13. 12. N. Datta, R. Fernández, J. Fröhlich, and L. Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy. Helv. Phys. Acta 69:752-820, 1996. Reprinted in The Mathematical Side of the Coin. Essays in Mathematical Physics (Birkhäuser, 1996).
14. 13. R. L. Dobrushin, Existence of a phase transition in the two-dimensional and three-dimensional Ising models, Soviet Phys. Doklady 10:111-113 (1965).
15. 14. H. Eskes, A. M. Olés, M. B. J. Meinders, and W. Stephan, Spectral properties of the Hubbard model, Phys. Rev. B 50:17980-8002 (1994).
16. 15. K. Friedrichs, Perturbation of Spectra in Hilbert Space, Am. Math. Soc. (Providence, R.I., 1965).
17. 16. J. Fröhlich and L. Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. III. Eamples. Helv. Phys. Acta 69:821-849, 1996. Reprinted in The Mathematical Side of the Coin. Essays in Mathematical Physics (Birkhäuser, 1996).
18. 4: interaction in three dimensions, Commun. Math. Phys. 10:1-47 (1968).
19. 18. R. B. Griffiths, Peierls' proof of spontaneous magnetization of a two-dimensional Ising ferromagnet, Phys. Rev. A 136:437-439 (1964).
20. 19. C. Gross, R. Joynt, and T. M. Rice, Antiferromagnetic correlations in almost-localized Fermi liquids, Phys. Rev. B 36:381-93 (1987).
21. 20. C. Gruber, J. Iwanski, J. Jedrzejewski, and P. Lemberger, Ground states of the spinless Falicov Kimball model, Phys. Rev. B 41:2198-209 (1990).
22. 21. C. Gruber, J. Jȩdrzejewski, and P. Lemberger, Ground states of the spinless Falicov Kimball model. II, J. Statist. Phys. 66:913-38 (1992).
23. 22. C. Gruber and N. Macris, The Falicov-Kimball model: A review of exact results and extensions, Helv. Phys. Acta 69:850-907 (1996). Reprinted in The Mathematical Side of the Coin. Essays in Mathematical Physics (Birkhäuser, 1996).
24. 23. C. Gruber, N. Macris, A. Messager, and D. Ueltschi, Ground states and flux configurations of the two-dimensional Falicov-Kimball model, J. Statist. Phys. 86:57-108 (1997).
25. 24. C. Gruber and A. Sütö, Phase diagrams of lattice systems of residual entropy, J. Stat. Phys. 42:113-142 (1988).
26. 25. C. Gruber, D. Ueltschi and J. Jȩdrzejewski, Molecule formation and the Farey tree in the one-dimensional Falicov-Kimball model. J. Stat. Phys. 76:125-157 (1994).
27. 26. A. B. Harris and R. V. Lange, Single-particle excitations in narrow energy bands, Phys. Rev. 157:295-314 (1967).
28. 27. W. Holsztynski and J. Slawny, Peierls condition and the number of ground states, Common. Math. Phys. 61:177-190 (1978).
29. 4 using a constrained-density-functional approach. Phys. Rev. B 39:9028-41 (1989).
30. 29. M. Hybertsen, E. B. Stechel, M. Schlüter, and D. R. Jennison, Renormalization from density functional theory to strong-coupling models for electronic states in Cu-O materials. Phys. Res. B 41:11068-72 (1990).
31. 30. T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Berlin/Heidelberg/ New York, 1966).
32. 31. T. Kennedy, Some rigorous results on the ground states of the Falicov-Kimball model, Rev. Math. Phys. 6:901-25 (1694).
33. 32. T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long range order, Physica A 138:320-58 (1986).
34. 33. D. J. Klein and W. A. Seitz, Perturbation expansion of the linear Hubbard model, Phys. Rev. B 8:2236-47 (1973).
35. 34. R. Kotecký, L. Laanait, A. Messager, and S. Miracle-Solé, A spin-1 lattice model of microemulsions at low temperatures, J. Phys. A 26:5285-93 (1993).
36. 35. R. Kotecký and D. Ueltschi, Effective interactions due to quantum fluctuations. Preprint (1998), can be retrieved from http://www.ma.utexas.edu/mp arc/, preprint 98-258.
37. 36. J. L. Lebowitz and N. Macris, Long range order in the Falicov-Kimball model: Extension of Kennedy-Lieb theorem, Rev. Math. Phys. 6:927-46 (1994).
38. 37. A. H. MacDonald, S. M. Girvin, and D. Yoshioka, t/U expansion for the Hubbard model, Phys. Rev. B 37:9753-6 (1988).
39. 38. A. Messager and S. Miracle-Solé, Low temperature states in the Falicov-Kimball model, Rev. Math. Phys. 8:271-99 (1996).
40. 39. R. Peierls, Ising's model of ferromagnetism. Proc. Cambridge Philos. Soc. 32:477-481 (1936).
41. 40. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Continuation, Theor. Math. Phys. 26:39-49 (1976). [Russian original: Theor. Mat. Fiz. 26:61-76 (1976)].
42. 40. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Continuation, Theor. Math. Phys. 26:39-49 (1976). [Russian original: Theor. Mat. Fiz. 26:61-76 (1976)].
43. 41. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems. I. Theor. Math. Phys. 25:1185-92 (1976). [Russian original: Theor. Mat. Fiz. 25:358-69 (1975)].
44. 41. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems. I. Theor. Math. Phys. 25:1185-92 (1976). [Russian original: Theor. Mat. Fiz. 25:358-69 (1975)].
45. 42. M. Reed and B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators (Academic Press, New York London, 1978).
46. 43. Ya. G. Sinai, Theory of Phase Transitions: Rigorous Results (Pergamon Press, Oxford/ New York, 1982).
47. 44. J. Slawny, Low temperature properties of classical lattice systems: phase transitions and phase diagrams, in Phase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London/New York, 1985).
48. 45. M. Takahashi, Half-filled Hubbard model at low temperatures, J. Phys. C 10:1289-301 (1977).
49. 46. H. Tasaki, The Hubbard model: Introduction and some rigorous results, Markov Proc. Rel. Fields 2:183-208 (1996).
50. 47. G. I. Watson and R. Lemanski, The ground-state phase diagram of the two-dimensional Falicov Kimball model, J. Phys. Condens. Matter 7:9521-42 (1994).