Gauge theory of the Hubbard model on honeycomb lattice and its instanton effect

TL;DR

This paper explores the spin disordered phase in the Hubbard model on a honeycomb lattice, revealing that instanton effects destabilize the phase and induce translation symmetry breaking.

Contribution

It introduces a gauge theory framework including instanton effects to analyze the stability of spin disordered phases in the Hubbard model.

Findings

Identifies a meanfield spin disordered phase in the Hubbard model.

Shows instanton proliferation leads to instability and symmetry breaking.

Calculates instanton quantum numbers and their effects on phase stability.

Abstract

In this paper we investigate possible spin disordered phase in the Hubbard model on the honeycomb lattice. Using a slave-particle theory that include the charge fluctuations, we find a meanfield spin disordered phase in a range of on-site repulsion $U$. The spin disordered state is described by gapped fermions coupled to compact U(1) gauge field. We study the confinement/deconfinement problem of the U(1) gauge theory due to the instantons proliferation. We calculate all allowed instanton terms and compute their quantum numbers. It is shown that the meanfield spin disordered phase is unstable. The instantons proliferation induce a translation symmetry breaking.