Infinite matrix product states for $(1+1)$-dimensional gauge theories

TL;DR

This paper introduces a matrix product operator framework for representing lattice gauge theory Hamiltonians, enabling the study of infinite lattice systems with symmetric matrix product states.

Contribution

It develops link-enhanced matrix product operators (LEMPOs) for local, translation-invariant Hamiltonian representation in gauge theories, including non-abelian cases.

Findings

Successfully applied to the Schwinger model with massless and massive fermions.

Extended to adjoint QCD$_2$, demonstrating versatility.

Provides a new computational tool for infinite lattice gauge theories.

Abstract

We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD$_2$.