Gauge invariance, correlated fermions, and photon mass in 2+1 dimensions

TL;DR

This paper introduces an exactly solvable 2+1D quantum gauge theory with correlated fermions, revealing massive photons and a spectrum with both gapped and gapless modes, relevant for understanding partially gapped fermions on a lattice.

Contribution

The paper develops a novel exactly solvable gauge theory model in 2+1 dimensions that incorporates correlated fermions, density interactions, and dynamical photons, with implications for lattice systems.

Findings

Photons acquire mass due to gauge-invariant normal-ordering.

The model remains well-defined after renormalization in the continuum limit.

The excitation spectrum includes two gapped modes and one gapless mode.

Abstract

We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in two dimensional continuum space; this system has two dimensional character due to density-density interactions and due to a coupling to dynamical photons propagating in the continuous embedding space. We argue that this model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. Our results include the following: after non-trivial renormalizations of the coupling parameters, the model remains well-defined in the quantum field theory limit as the grid of lines becomes a continuum; the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model; the exact excitation spectrum of the model has two gapped and one gapless mode.