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

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.

Comments: 22 pages, 18 figures, RevTeX; v2: new data on larger lattices added, results updated; published version