Hubbard model with SU(4) symmetry

TL;DR

This paper introduces an SU(4)-invariant Hubbard model with nonlocal interactions, analyzing its phase transitions and thermodynamic properties, which resemble behaviors observed in high-temperature cuprate superconductors.

Contribution

It presents a tractable SU(4)-invariant Hubbard model unifying antiferromagnetic and d-wave superconducting orders, with analysis of phase transitions and thermodynamic properties.

Findings

Antiferromagnetic critical temperature peaks near half-filling

Superconductivity occurs when Fermi surface crosses high density of states area

Normal phase properties match experimental data in high-$T_c$ cuprates

Abstract

In the model considered, the nonlocal interaction of the fermions in different sublattices of a bipartite lattice is introduced. It can also be regarded as local interaction of fermions with opposite ``hypercharge''. The corresponding term in the Hamiltonian is SU(4)-invariant and appears to be the most tractable version of the SO(5)-invariant model that unifies antiferromagnetic and d-wave superconducting order parameters. The model has been studied primarily in the weak interaction limit and in the mean field approximation. Near the half-filling the antiferromagnetic critical temperature has a peak. However, the superconducting transition takes place when the Fermi surface crosses the area where the density of states is of order of inverse coupling coefficient. Thus, in mean-field approximation, there exist an interval of values of the chemical potential, for which the system is a superconductor for arbitrary high temperatures. The temperature dependence of specific heat, Hall coefficient, and DC conductivity in the normal phase agrees with that experimentally observed in high-$T_c$ cuprates.