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Physical review. B, Solid state

Thermodynamics of an extended Hubbard model chain. I: Atomic limit for the half-filled band

G. Beni, Philip A. Pincus

Published Apr 1, 1974• 65 citations
Publisher

Abstract

For an infinite linear chain we consider the atomic limit of an extended Hubbard model which take into account the nearest-neighbor interatomic electron-electron repulsion. The specific heat, static magnetic susceptibility, and density-density correlation function are studied exactly at any temperature for the half-filled-band case. We discuss also the quarter-filled band in the limit of infinite intra-atomic Coulomb repulsion.

DOI
10.1103/physrevb.9.2963

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For an infinite linear chain we consider the atomic limit of an extended Hubbard model which take into account the nearest-neighbor interatomic electron-electron repulsion. The specific heat, static magnetic susceptibility, and density-density correlation function are studied exactly at any temperature for the half-filled-band case. We discuss also the quarter-filled band in the limit of infinite intra-atomic Coulomb repulsion.
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.
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.
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.
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.
In order to investigate the thermal properties (specific heat, magnetic susceptibility, entropy, internal energy, and some correlation functions) of the one-dimensional half-filled-band Hubbard model, we have studied linear chains and rings containing two to six atoms, by performing machine calculations. Supplementing the low-temperature behavior obtained from the exact solution for the infinite chain by Lieb and Wu, our results should be suggestive of the properties of the infinite system throughout the entire temperature domain. It is shown that when the ratio of the correlation energy UUU to the total width $\ensuremath{\Delta}$ of the band of single-particle excitations is larger than 1, the specific heat has two peaks. The high-temperature peak arises from the gradual metal-insulator transition (or the gradual formation of local moments), while the low-temperature peak is associated with the antiferromagnetic short-range ordering. When $\frac{U}{\ensuremath{\Delta}}$ becomes small, the two peaks merge into one. This picture is consistent with all other thermal properties, including correlation functions. The high-temperature properties are compared with the results predicted by Hubbard's approximate theory based on the truncation of the equations of motion of the Green's functions.