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Acta Physica Sinica

THERMODYNAMIC PROPERTIES OF THE ONE-DIMENSIONAL EXTENDED HUBBARD MODEL(Ⅰ)——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• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.34.1422

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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.
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.
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.
The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility ${\ensuremath{\chi}}_{s},$ and charge susceptibility ${\ensuremath{\chi}}_{c}$ are studied as functions of temperature and doping within the two-dimensional Hubbard model with various U/t=4−−12.U/t=4--12.U/t=4−−12. Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density $n\ensuremath{\sim}1\ifmmode\pm\else\textpm\fi{}0.15$ in the whole regime of studied U/t.U/t.U/t. The pseudogap in ${\ensuremath{\chi}}_{s}(T)$ becomes clearly pronounced for U/t> 8U/t>~8U/t> 8 while ${\ensuremath{\chi}}_{c}$ shows a maximum close to half-filling. The relation of results to those within the $t\ensuremath{-}J$ model and to experiments is discussed.
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.
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.