Vacuum structure of gapped QCD$_2$ theories from the infinite Hamiltonian lattice

TL;DR

This paper employs tensor network methods to analyze the vacuum structure of gapped 2D gauge theories with massless fermions, confirming theoretical predictions and proposing a lattice decay rule to determine vacuum degeneracy.

Contribution

It introduces a lattice decay rule for identifying continuum vacua from strong-coupling lattice states in gapped 2D gauge theories.

Findings

Lattice results agree with previous theoretical predictions.

Identified strong-coupling states corresponding to degenerate vacua.

Proposed a general procedure to compute vacuum degeneracy from lattice Hamiltonians.

Abstract

Gapped two-dimensional gauge theories with massless fermions generically have rich vacuum structures consisting of many degenerate vacua related by the action of topological line operators. The algebra of such operators has been used to calculate ratios of vacuum expectation values of local operators and to predict nontrivial particle-soliton degeneracies. In this paper, we use recently-developed tensor network methods to study several examples of such theories via their Hamiltonian lattice descriptions. Our lattice results agree with all previously-made predictions. Furthermore, we identify the lattice strong-coupling states that can be adiabatically continued to the degenerate vacua in the continuum limit. We conjecture a procedure, referred to as a lattice decay rule, for how this identification works in general. This rule allows us to compute the continuum vacuum degeneracy by studying the lattice Hamiltonian in the strong-coupling limit.