Abstract
The dynamical mean-field approximation (DMFA) becomes exact in the limit of infinite dimensions, and allows results to be obtained in a nonperturbative regime without the limitations normally found with exact diagonalization (ED) and quantum Monte Carlo (QMC) methods. In this paper, we investigate the applicability of the method to lattices with small coordination number in special situations. Specifically we use this approximation to study the two-dimensional (2D) Hubbard model on a square lattice far from half filling. In this situation, we calculate the specific heat and find that when the filling decreases, that is, antiferromagnetic correlations become less important, the agreement between DMFA and QMC results increases. Our results show that the DMFA can be a valuable technique for studying the thermodynamic properties of the Hubbard model also on a square lattice, but within a parameter range in which the antiferromagnetic correlations are not important.
Highlights
Correlated electron systems (SCESs) present some of the most fascinating physical phenomena of condensedmatter physics
At half filling (n = 1), the dynamical mean-field approximation (DMFA) gives a qualitatively incorrect result because it predicts a Mott transition at Uc ≈ 12|t| [17]; we conclude that increases the quality of this approximation in the study of the 2D Hubbard model on a square lattice when the density n decreases
We calculate the dependence on temperature of the specific heat of the 2D Hubbard model on a square lattice far from half filling and compare it with quantum Monte Carlo (QMC) simulations
Summary
Correlated electron systems (SCESs) present some of the most fascinating physical phenomena of condensedmatter physics. They compared results for the spectral function obtained by using DMFA and QMC and have found that the DMFA gives a rather accurate description of the dynamical properties of the 2D Hubbard model on a square lattice, as long as long-range spin correlations are not important.
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