Real-space pairing in fermion systems

K. A. Penson; M. Kolb

doi:10.1103/PhysRevB.33.1663

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Real-space pairing in fermion systems

K. A. Penson and M. Kolb

Institute for Theoretical Physics, Freie Universitat Berlin, Arnimallee 14, D-1000 Berlin 33, West Germany

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Phys. Rev. B 33, 1663 – Published 1 February, 1986

DOI: https://doi.org/10.1103/PhysRevB.33.1663

Abstract

A real-space tight-binding model of fermions involving the competition between an attraction V between the localized fermion pairs on different sites and an ordinary one-particle hopping t is introduced. The ground-state properties of its one-dimensional version are studied with use of numerically exact finite-chain calculations for up to N=10 sites. A transition of the essential singularity type between the band and the localized-pairs state is found for finite V/t.

References (20)

J. Bardeen, L. N.Cooper and J. R. Schrieffer, Phys. Rev. 106, 162 (1957); ibid. 108, 1175 (1957).
E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics (Pergamon, Oxford, 1980), Pt. 2.
G. E. Brown, Unified Theory of Nuclear Models and Forces (North Holland, Amsterdam, 1967); V. G. Soloviev, Theory of Complex Nuclei (Pergamon, Oxford, 1976).
D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic, New York, 1972), Chap. 7. C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963), Chap. 8.
J. Appel and W. Kohn, Phys. Rev. B 4, 2162 (1971); A. Birnboim and H. Gutfreund, ibid. 9, 139 (1974).
P. W. Anderson, Phys. Rev. Lett. 34, 953 (1975).
A. Alexandrov and J. Ranninger, Phys. Rev. B 24, 1164 (1981); B. K. Chakraverty, Ferroelectrics 53, 59 (1984); D. Feinberg, thesis, University of Grenoble, 1984, and references therein.
S. Robaszkiewicz, R. Micnas and K. A. Chao, Phys. Rev. B 26, 3915 (1982).
B. Ya. Moizhes and I. A. Drabkin, Fiz. Tverd. Tela (Leningrad) 25, 1974 (1983) [Sov. Phys.—Solid State 25, 1139 (1983)]; V. V. Bryksin, V. S. Voloshin and A. V. Raitsev, ibid., 25, 1427 (1983) [ 25, 820 (1983)].
P. Pincus, P. Chaikin and C. F. Coll, III, Solid State Commun. 12, 1265 (1973).
J. Friedel and C. Noguera, Int. J. Quant. Chem. 23, 1209 (1983).
V. Ya. Krivnov and A. A. Ovchinnikov, Zh. Eksp. Teor. Fiz. 67, 1568 (1974) [Sov. Phys.—JETP 40, 781 (1975)].
P. Nozières and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985).
I. O. Kulik and A. G. Pedan, Zh. Eksp. Teor. Fiz. 79, 1469 (1980) [Sov. Phys.—JETP 52, 742 (1980)].
Since V describes the hopping of pairs it may be t dependent. For the purpose of studying the transition we assume V and t to be independent.
E. Lieb and D. C. Mattis, Phys. Rev. 125, 164 (1962).
Since (3) involves two- and four-body interactions, it reminds the reader of the one-dimensional version of the Ashkin-Teller model with quantum XY symmetry.
R. Jullien and P. Pfeuty, J. Phys. A 14, 3111 (1981); H. J. Herrmann and H. O. Màrtin, ibid. 17, 657 (1984).
M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8.
C. J. Thompson, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. G. Green (Academic, London, 1972), Vol. 1.

[c1] J. Bardeen, L. N.Cooper and J. R. Schrieffer, Phys. Rev. 106, 162 (1957); ibid. 108, 1175 (1957).

[c2] E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics (Pergamon, Oxford, 1980), Pt. 2.

[c3] G. E. Brown, Unified Theory of Nuclear Models and Forces (North Holland, Amsterdam, 1967); V. G. Soloviev, Theory of Complex Nuclei (Pergamon, Oxford, 1976).

[c4] D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic, New York, 1972), Chap. 7. C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963), Chap. 8.

[c5] J. Appel and W. Kohn, Phys. Rev. B 4, 2162 (1971); A. Birnboim and H. Gutfreund, ibid. 9, 139 (1974).

[c6] P. W. Anderson, Phys. Rev. Lett. 34, 953 (1975).

[c7] A. Alexandrov and J. Ranninger, Phys. Rev. B 24, 1164 (1981); B. K. Chakraverty, Ferroelectrics 53, 59 (1984); D. Feinberg, thesis, University of Grenoble, 1984, and references therein.

[c8] S. Robaszkiewicz, R. Micnas and K. A. Chao, Phys. Rev. B 26, 3915 (1982).

[c9] B. Ya. Moizhes and I. A. Drabkin, Fiz. Tverd. Tela (Leningrad) 25, 1974 (1983) [Sov. Phys.—Solid State 25, 1139 (1983)]; V. V. Bryksin, V. S. Voloshin and A. V. Raitsev, ibid., 25, 1427 (1983) [ 25, 820 (1983)].

[c10] P. Pincus, P. Chaikin and C. F. Coll, III, Solid State Commun. 12, 1265 (1973).

[c11] J. Friedel and C. Noguera, Int. J. Quant. Chem. 23, 1209 (1983).

[c12] V. Ya. Krivnov and A. A. Ovchinnikov, Zh. Eksp. Teor. Fiz. 67, 1568 (1974) [Sov. Phys.—JETP 40, 781 (1975)].

[c13] P. Nozières and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985).

[c14] I. O. Kulik and A. G. Pedan, Zh. Eksp. Teor. Fiz. 79, 1469 (1980) [Sov. Phys.—JETP 52, 742 (1980)].

[c15] Since V describes the hopping of pairs it may be t dependent. For the purpose of studying the transition we assume V and t to be independent.

[c16] E. Lieb and D. C. Mattis, Phys. Rev. 125, 164 (1962).

[c17] Since (3) involves two- and four-body interactions, it reminds the reader of the one-dimensional version of the Ashkin-Teller model with quantum XY symmetry.

[c18] R. Jullien and P. Pfeuty, J. Phys. A 14, 3111 (1981); H. J. Herrmann and H. O. Màrtin, ibid. 17, 657 (1984).

[c19] M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8.

[c20] C. J. Thompson, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. G. Green (Academic, London, 1972), Vol. 1.

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