Dual Lattice Simulation of the Abelian Gauge-Higgs Model at Finite Density: An Exploratory Proof of Concept Study

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 nonzero contributions. We simulate the model in the dual representation using a generalized worm algorithm, explore the phase diagram, and study condensation phenomena at finite $\mu$.

Figure 1

The observables $⟨U⟩$, $⟨|\varphi {|}^2⟩$, and ${\chi }_{n_{\varphi }}$ (left to right) as functions 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 ${\chi }_{\varphi }$ and the inflection points of ${\chi }_n$. We also mark points where we performed runs at finite $\mu$ (plus signs labeled $a$ to $h$).

Figure 3

From left to right we show the observables $⟨U⟩$, $⟨|\varphi {|}^2⟩$, $n$, 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).