Symmetries of an Extended Hubbard Model

TL;DR

This paper investigates the symmetries of an extended Hubbard model with phonons, revealing a superconducting SU_q(2) quantum symmetry in one dimension under specific conditions, and discusses implications for phonon coupling.

Contribution

It identifies conditions under which the extended Hubbard model exhibits a quantum SU_q(2) symmetry, especially in one dimension, and connects this to phonon coupling and mean field approximations.

Findings

Superconducting SU_q(2) symmetry exists in 1D for specific parameters.

Quantum symmetric Hubbard model without phonons can be derived via mean field.

Symmetry depends on the vanishing of local phonon coupling.

Abstract

An extended Hubbard model with phonons is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the parameters a superconducting SU_q(2) holds as a true quantum symmetry - but only for D=1. In a natural basis the symmetry requires vanishing local phonon coupling; a quantum symmetric Hubbard model without phonons can then be obtained by a mean field approximation.