Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion

TL;DR

This paper uses quantum Monte Carlo simulations to explore a phase transition between two topologically distinct phases, revealing an intermediate gapless phase with stripe order that exhibits deconfined $U(1)$ gauge behavior.

Contribution

It provides evidence for a gapless deconfined $U(1)$ gauge theory at the transition between toric code and double semion phases in a 2D model.

Findings

Discovery of an intermediate stripe-ordered phase

Evidence of a gapless phase with incommensurate stripe pattern

Identification of a $U(1)$ gauge theory with Cantor deconfinement

Abstract

Building on quantum Monte Carlo simulations, we study the phase diagram of a one-parameter Hamiltonian interpolating between trivial and topological Ising paramagnets in two dimensions, which are dual to the toric code and the double semion. We discover an intermediate phase with stripe order which spontaneously breaks the protecting Ising symmetry. Remarkably, we find evidence that this intervening phase is gapless due to the incommensurability of the stripe pattern and that it is dual to a $U(1)$ gauge theory exhibiting Cantor deconfinement.