Topological multicritical point in the Toric Code and 3D gauge Higgs Models

TL;DR

This paper identifies a new multicritical point in 3D gauge Higgs models and the 2D quantum toric code, characterized by competing Higgs and confinement transitions, with phase diagrams analyzed via Monte Carlo simulations.

Contribution

It reveals a novel multicritical point arising from Higgs and confinement transition competition, and maps this phenomenon to the 2D quantum toric code with external fields.

Findings

Transition lines are second-order until merging into a first-order line.

Phase diagram features a multicritical point with noncommuting order parameters.

Predicted similar phase diagram for the 2D quantum toric code model.

Abstract

We report a new type of multicritical point that arises from competition between the Higgs and confinement transitions in a Z_2 gauge system. The phase diagram of the 3d gauge Higgs model has been obtained by Monte-Carlo simulation on large (up to 60^3) lattices. We find the transition lines continue as 2nd-order until merging into a 1st-order line. These findings pose the question of an effective field theory for a multicritical point involving noncommuting order parameters. A similar phase diagram is predicted for the 2-dimensional quantum toric code model with two external fields, h_z and h_x; this problem can be mapped onto an anisotropic 3D gauge Higgs model.