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Physical review. B, Solid state

Strong-Coupling Hubbard Chain

G. Beni, Theodore D. Holstein, Philip A. Pincus

Published Jul 1, 1973• 93 citations
Publisher

Abstract

An exact expression is obtained for the partition function of the arbitrary-electron-density Hubbard chain in the infinite-coupling ($U\ensuremath{\rightarrow}\ensuremath{\infty}$) limit. It is shown that the magnetic susceptibility obeys a Curie law, while the orbital contribution to the specific heat corresponds to that of a noninteracting band of spinless fermions. The electronic mobilities in this limit are shown to be infinite.

DOI
10.1103/physrevb.8.312

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Physical review. B, Solid state•Feb 15, 1974•0 citations
An exact expression is obtained for the partition function of the arbitrary-electron-density Hubbard chain in the infinite-coupling (U\ensuremath→\ensuremath∞U\ensuremath{\rightarrow}\ensuremath{\infty}U\ensuremath→\ensuremath∞) limit. It is shown that the magnetic susceptibility obeys a Curie law, while the orbital contribution to the specific heat corresponds to that of a noninteracting band of spinless fermions. The electronic mobilities in this limit are shown to be infinite.
For an infinite linear chain we consider the strong-coupling ($U\ensuremath{\rightarrow}\ensuremath{\infty}$) limit of an extended Hubbard Hamiltonian which takes into account the nearest-neighbor interatomic Coulomb repulsion. It is shown that the magnetic susceptibility obeys a Curie law, and, to this effect, a theorem is proved pertaining to the partition function. The specific heat is computed for the quarter-filled band to lowest order in the transfer integral. The density-density correlation function and the specific heat are also obtained in the atomic limit for an arbitrary density.
I observe that the high-temperature expansions of the U=\ensuremath{\infty} Hubbard model on two- and three-dimensional bipartite lattices are consistent with a strong separation of energy scales for spin and translational degrees of freedom at an electron density n near 8/11. The high-temperature expansion of the specific heat is nearly identical with the high-temperature expansion of spinless fermionic holes of density 1-n, while the expansion of the uniform magnetic susceptibility is nearly identical with the susceptibility of free spins. Previous finite-size calculations are also consistent with this result.
All the three-electron wave functions and energy levels are obtained for the one-dimensional Hubbard model. The second and third virial coefficients for the system are calculated exactly. The virial expansion is converted into an electron density expansion which appears to converge much better than the virial series. The two-particle and three-particle contributions to the specific heat, entropy, intra-atomic correlation function, and magnetic susceptibility of the system are obtained and presented graphically.