Discrete Symmetries and Transformations of the Hubbard Model

TL;DR

This paper uncovers discrete symmetries in the half-filled Hubbard model on bipartite lattices, revealing new transformations and a symmetric Hubbard-Stratonovich decomposition that impact mean field and renormalization analyses.

Contribution

It identifies a new group of discrete symmetries in addition to SO(4) and introduces a symmetric Hubbard-Stratonovich decomposition incorporating spin and pseudospin.

Findings

Discrete symmetries extend beyond SO(4) in the Hubbard model.

A symmetric Hubbard-Stratonovich decomposition is constructed.

Implications for mean field and renormalization group analyses are discussed.

Abstract

We show that, in addition to SO(4), the Hubbard model at half filling on a bipartite lattice has a group of discrete symmetries and transformations. A unique Hubbard-Stratonovich decomposition of the interaction term, incorporating both spin and pseudospin variables on an equal footing, is found in which these symmetries are manifestly present. The consequences of this at the mean field and one loop renormalisation group levels are discussed.