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Journal of Physics A Mathematical and General

Thermodynamics of the strongly correlated Hubbard model

Sam Y. S. Yang, Colin J. Thompson

Published Mar 21, 1991• 10 citations
Publisher

Abstract

High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.

DOI
10.1088/0305-4470/24/6/006

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High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.
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.
The effect of spin polarization in the slave boson mean field theory in the strongly correlated Heavy electron systems is discussed concerning the thermodynamical properties of the Hubbard model. The free energy is evaluated by taking into account the effective reduction of the quantum states due to the exclusion of double occupation in a site through the introduction of the spin-dependent slave boson. The magnetic susceptibility, calculated as a function of temperature, shows the Fermi liquid property at low temperature and the local moment behaviour with the proper Curie constant at high temperature. The present results, including the temperature dependence of the specific heat, are compared with the previous results without the reduction of quantum states.
The authors show with the aid of a canonical transformation that separates charge and spin degrees of freedom that the strongly correlated one-dimensional Hubbard model with infinite (U= infinity ) on-site repulsion is related to a corresponding spinless free-fermion lattice model. Thermodynamic properties of the two models are shown to be closely related whereas the single-particle two-site function for the U= infinity model is shown to be related to a modified many site function for the spinless model which involves many-point correlations. The latter is shown to be expressible in terms of the inverse of a certain matrix which should be amenable to numerical and analytical analysis.
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.