Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States

TL;DR

This paper uses gauge invariant tensor network methods to map the phase diagram of square ice, a 2D U(1) lattice gauge theory, and reveals that string excitations are described by a conformal field theory.

Contribution

It introduces gauge invariant matrix product states to analyze square ice, providing new insights into its phase transitions and the nature of string excitations.

Findings

Good agreement with previous phase diagram studies

String excitations are described by a conformal field theory

Tensor network methods are effective for 2D lattice gauge theories

Abstract

We investigate the ground state phase diagram of square ice -- a U(1) lattice gauge theory in two spatial dimensions -- using gauge invariant tensor network techniques. By correlation function, Wilson loop, and entanglement diagnostics, we characterize its phases and the transitions between them, finding good agreement with previous studies. We study the entanglement properties of string excitations on top of the ground state, and provide direct evidence of the fact that the latter are described by a conformal field theory. Our results pave the way to the application of tensor network methods to confining, two-dimensional lattice gauge theories, to investigate their phase diagrams and low-lying excitations.