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Physical review. B, Solid state

Thermodynamics of an extended Hubbard-model chain. II. Strong-coupling limit

J.-P. Gallinar

Published Jun 1, 1975• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.11.4421

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Physical review. B, Solid state•Oct 15, 1974•17 citations
For an infinite linear chain we consider the strong-coupling (U\ensuremath→\ensuremath∞U\ensuremath{\rightarrow}\ensuremath{\infty}U\ensuremath→\ensuremath∞) 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.
In order to determine finite-temperature properties of the infinite one-dimensional Hubbard model for the half-filled band, finite systems such as chains with 2 to 5 atoms and rings with 4 and 6 atoms are studied with the application of the grand canonical ensemble. The obtained temperature dependence of the specific heat, the entropy, the magnetic susceptibility and some correlation functions clearly shows a rearrangement of the electronic state of the system with the increase of the strength of the Coulomb interaction relative to the transfer integral. In the light of our new results the functional integral approach recently proposed by Kimball and Schrieffer as well as Hubbard's approximate theory is examined.
The dimerized-chain Hubbard model is characterized by a Coulomb energy UUU and two alternating transfer constants, an intradimer constant ttt, and a smaller interdimer constant ${t}^{\ensuremath{'}}$. We have used thermodynamic perturbation theory to treat the half-filled-band case, taking the interdimer transfer as the perturbation term. The unperturbed problem is a lattice of isolated dimers. We give the energy, specific heat, and magnetic susceptibility as functions of temperature for the unperturbed case and for the first nonvanishing order in the perturbation. The results are consistent with the U=0U=0U=0 case, which is solved exactly. The interdimer transfer ${t}^{\ensuremath{'}}$ has the effect of distorting the peaks in the specific heat and reducing the susceptibility; this is shown graphically.