Electric conductivity in finite-density <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> lattice gauge theory with dynamical fermions
P. V. Buividovich, Dominik Smith, Lorenz von Smekal
Abstract
We study the dependence of the electric conductivity on chemical potential in finite-density $SU(2)$ gauge theory with ${N}_{f}=2$ flavors of rooted staggered sea quarks, in combination with Wilson-Dirac and domain-wall valence quarks. The pion mass is reasonably small with ${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}\ensuremath{\approx}0.4$. 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 $\ensuremath{\sigma}(T,\ensuremath{\mu})=\ensuremath{\sigma}(T,0)(1+c(T){(\ensuremath{\mu}/T)}^{2}+O({\ensuremath{\mu}}^{4}))$ in powers of $\ensuremath{\mu}$, which has rather weak temperature dependence and takes its maximal value $c(T)\ensuremath{\approx}0.10\ifmmode\pm\else\textpm\fi{}0.07$ around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows toward 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 ${T}_{c}/{m}_{\ensuremath{\pi}}\ensuremath{\approx}0.4$ at $\ensuremath{\mu}=0$ is significantly smaller than in real QCD.