Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions

TL;DR

This study investigates how electric conductivity varies with chemical potential in finite-density SU(2) lattice gauge theory, revealing sensitivity near the chiral crossover and providing estimates for conductivity expansion coefficients.

Contribution

It offers the first estimate of the coefficient c(T) in the conductivity expansion near the chiral crossover in SU(2) gauge theory with dynamical fermions.

Findings

Electric conductivity is most sensitive to small density changes near the chiral crossover.

The coefficient c(T) has weak temperature dependence and peaks around the critical temperature.

Conductivity approaches free quark results at higher densities and lower temperatures.

Abstract

We study the dependence of the electric conductivity on chemical potential in finite-density $SU(2)$ gauge theory with $N_f = 2$ flavours of rooted staggered sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks. The pion mass is reasonably small with $m_{\pi}/m_{\rho} \approx 0.4$. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient $c(T)$ of the expansion of conductivity $\sigma(T,\mu) = \sigma(T,0) \left(1 + c(T) (\mu/T)^2 + O(\mu^4)\right)$ in powers of $\mu$, which has rather weak temperature dependence and takes its maximal value $c(T) \approx 0.10 \pm 0.07$ around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows towards the diquark condensation phase, and also becomes closer to the free quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for $SU(2)$ gauge theory the ratio of crossover temperature to pion mass $T_c/m_{\pi} \approx 0.4$ at $\mu=0$ is significantly smaller than in real QCD.