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Acta Physica Sinica

THERMODYNAMIC PROPERTIES OF THE ONE-DIMENSIONAL EXTENDED HUBBARD MODEL (Ⅱ)——U<0

XU HUI, Kaiyi Zhang, (1)东北工学院物理系; (2)中南矿冶学院数理系

Published Jan 1, 1985• 0 citations
Publisher

Abstract

Entropy, internal energy, specific heat, and magnetic susceptibility of the one-dimensional negative-U extended Hubbard model are computed. An analytical solution of magnetic susceptibility in the strong-coupling (|U|→∞) limit is obtained. Therma-dynamic properties of the system can be discussed in two temperature regions. The high T-region corresponds to decrease in number of double occupied states. The low T-region corresponds to the distribution of electron charge. The effect of W on the-rmodynamic properties is obvious.

DOI
10.7498/aps.34.1433

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Entropy, internal energy, specific heat, and magnetic susceptibility of the one-dimensional negative-U extended Hubbard model are computed. An analytical solution of magnetic susceptibility in the strong-coupling (|U|→∞) limit is obtained. Therma-dynamic properties of the system can be discussed in two temperature regions. The high T-region corresponds to decrease in number of double occupied states. The low T-region corresponds to the distribution of electron charge. The effect of W on the-rmodynamic properties is obvious.
A perturbation expansion for the thermodynamic potential is performed to the third order by HTSE method. Entropy, internal energy, specific heat, and magnetic susceptibility of the one-dimensional extended Hubbard model are computed as functions of temperature, electron density, and t, U, W. Thermodynamics can be discussed in two temperature regions. The high T-region corresponds to increase in number of double occupied states. The low T-region corresponds to the distribution of electron spin. The effect of t on thermodynamic properties is obvious.
In order to contribute to understand well the thermodynamic properties of strongly correlated electron systems, we study numerically, in the grand canonical ensemble, the temperature dependence of the internal energy, specific heat, entropy, magnetization, and magnetic susceptibility of the one-dimensional Hubbard model without transference of moment in the interactions. The results have been obtained for a wide range of values of the on-site Coulombian repulsion U and of the external magnetic field h. Differences between this model and the original Hubbard model have been observed in relation to the number of peaks of the specific heat and to the behavior of the susceptibility in temperatures tending to zero. These differences evidence that the two models possess different magnetic structures of correlation.
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.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.