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arXiv:cond-mat/9609152 · Physical review. B, Condensed matter

Phase separation in the two-dimensional Hubbard model

Gang Su

Published Sep 15, 1996• 23 citations
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Abstract

By making use of known exact results and symmetry properties for the one-band Hubbard model, we show in a somewhat exact manner that there is no phase separation on a square lattice at arbitrary fillings at finite temperature for both attractive and repulsive on-site Coulomb interaction. This result is consistent with the quantum Monto Carlo calculation.

DOI
10.1103/physrevb.54.r8281

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By making use of known exact results and symmetry properties for the one-band Hubbard model, we show in a somewhat exact manner that there is no phase separation on a square lattice at arbitrary fillings at finite temperature for both attractive and repulsive on-site Coulomb interaction. This result is consistent with the quantum Monto Carlo calculation.
In this paper, we study phase separation in the two-dimensional single-band Hubbard model with the unrestricted Hartree-Fock(UHF) method and the restricted Hartree-Fock (RHF) method. We perform the calculation for square lattices and rectangle lattices. It is observed that the stripe phase exists and it depends on three aspects: geometry of the lattice, Coulomb interaction U and band filling n. To gain more physical insights, we consider the Hubbard model with spin dependent hoppings: t↑ and t↓, and study the effect of varying [Formula: see text] on the phase separation.
Inhomogeneities on various length scales suggesting phase separation seem to be a generic feature of hole-doped high-temperature superconducting cuprates. Also firmly established is the d-wave symmetry of the superconducting state. The interplay of superconductivity and phase separation has been noted in previous mean-field studies of correlated electron models. To further explore this issue in a more rigorous approach we have conducted quantum Monte Carlo calculations of a two-dimensional Hubbard model with nearest-neighbor attractive interaction. For a vanishing on-site repulsion, the result agrees with that of Micnas, Ranninger, and Robaszkiewicz [Phys. Rev. B 39, 11 653 (1989)], and indicates that for a given strength of the attractive interaction, homogeneous d-wave superconducting phase can exist only above a critical doping concentration, below which phase separation occurs. A finite on-site repulsion modifies the phase separation behavior. A stronger d-wave pairing correlation is seen in the inhomogeneous phase compared to the homogeneous phase.
On the Impossibility of Electronic Phase Separation in the D=1,2D=1,2D=1,2 Dimensional Hubbard Model at T=0
We show explicitly that the one- and two-dimensional Hubbard model does not show phase separation at any filling at T=0. Apart from a single plausible assumption, only known exact results and symmetry properties for the one-band Hubbard model are used. Implications for usage of the simple one-band Hubbard model for analysing the physics of cuprate superconductors are discussed. We also discuss models where electronic phase separation might generically occur, in the specific context of colossal magneto-resistance manganites.
We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.