Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study

TL;DR

The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical potential is mapped exactly to a dual representation where matter fields correspond to loops of flux and the gauge fields are represented by surfaces.

Abstract

The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical potential is mapped exactly to a dual representation where matter fields correspond to loops of flux and the gauge fields are represented by surfaces. The complex action problem of the conventional formulation at finite chemical potential mu is overcome in the dual representation and the partition sum has only real and non-zero contributions. We simulate the model in the dual representation using a generalized worm algorithm, explore the phase diagram and study condensation phenomena at finite mu.

Figures (3)

• Figure 1: The observables $\langle U \rangle$, $\langle |\phi|^2 \rangle$ and $\chi_{n_\phi}$ (left to right) as function of the inverse gauge coupling $\beta$ and mass parameter $M^2$.
• Figure 2: Phase diagram in the $\beta$-$M^2$ plane at $\mu = 0$. We show the phase boundaries determined from the maxima of $\chi_U$ and $\chi_{\phi}$ and the inflection points of $\chi_n$. We also mark points where we performed runs at finite $\mu$ (plus-signs labelled $a$ to $h$).
• Figure 3: From left to right we show the observables $\langle U \rangle$, $\langle |\phi|^2 \rangle$, $n$ and the average dual variables (normalized with factors as given in the legends) as a function of $\mu$ for points $b$ ($\beta = 0.75, M^2 = 5.73$, top row) and $d$ ($\beta = 0.75, M^2 = 4.92$, bottom row).