Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta = \pi\,$: Critical endpoint behavior

TL;DR

This paper uses dual lattice simulations to study the 2d U(1) gauge Higgs model at topological angle $ heta = \pi$, identifying a critical endpoint and confirming its 2d Ising universality class through finite size scaling.

Contribution

It introduces a dual representation approach to simulate the model at $ heta = \pi$, accurately capturing the topological effects and phase transition behavior.

Findings

Identifies the critical endpoint as a function of the scalar mass parameter.

Confirms the phase transition at $ heta = \\pi$ is in the 2d Ising universality class.

Demonstrates the effectiveness of the Villain action-based dual simulation method.

Abstract

We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle $\theta$. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a $\theta$-term. The Villain action is interpreted as a non-compact gauge theory whose center symmetry is gauged and has the advantage that the topological term is correctly quantized so that $2\pi$ periodicity in $\theta$ is intact. Because of this the $\theta = \pi$ theory has an exact $Z_2$ charge-conjugation symmetry $C$, which is spontaneously broken when the mass-squared of the scalars is large and positive. Lowering the mass squared the symmetry becomes restored in a second order phase transition. Simulating the system at $\theta = \pi$ in its dual form we determine the corresponding critical endpoint as a function of the mass parameter. Using a finite size scaling analysis we determine the critical exponents and show that the transition is in the 2d Ising universality class, as expected.