Crystalline phases at finite winding densities in a quantum link ladder

TL;DR

This paper uses tensor network methods to study the phase structure of a U(1) gauge invariant quantum link ladder at finite winding densities, revealing crystalline electric flux patterns and proposing experimental detection methods.

Contribution

It introduces a tensor network approach to analyze finite density phases of Abelian gauge theories without dynamical matter, focusing on flux crystallization and transition detection.

Findings

Crystalline patterns of electric flux tubes in the ground state.

Control of flux pattern period via external electric field.

Detection strategies for phase transitions in cold-atom experiments.

Abstract

Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult to study in Monte Carlo simulations when they are afflicted by a sign problem. As an alternate approach, we use tensor network methods to explore the finite density physics of Abelian gauge theories without dynamical matter. As a concrete example, we consider the U(1) gauge invariant quantum link ladder with spin-1/2 gauge fields in an external electric field which cause the winding electric fluxes to condense in the ground state. We demonstrate how the electric flux tubes arrange themselves in the bulk giving rise to crystalline patterns, whose period can be controlled by tuning the external field. We propose observables to detect the transitions in ground state properties not only in numerical experiments, but also in future cold-atom realizations. A systematic procedure for reaching the thermodynamic limit, as well as extending the studies from ladders to extended geometries is outlined.