# Low-Temperature Transport in Out-of-Equilibrium XXZ Chains. (arXiv:1711.00519v2 [cond-mat.stat-mech] UPDATED)

We study the low-temperature transport properties of out-of-equilibrium XXZ

spin-$1/2$ chains. We consider the protocol where two semi-infinite chains are

prepared in two thermal states at small but different temperatures and suddenly

joined together. We focus on the qualitative and quantitative features of the

profiles of local observables, which at large times $t$ and distances $x$ from

the junction become functions of the ratio $\zeta=x/t$. By means of the

generalized hydrodynamic equations, we analyse the rich phenomenology arising

by considering different regimes of the phase diagram. In the gapped phases,

variations of the profiles are found to be exponentially small in the

temperatures but described by non-trivial functions of $\zeta$. We provide

analytical formulae for the latter, which give accurate results also for small

but finite temperatures. In the gapless regime, we show how the three-step

conformal predictions for the profiles of energy density and energy current are

naturally recovered from the hydrodynamic equations. Moreover, we also recover

the recent non-linear Luttinger liquid predictions for low-temperature

transport: universal peaks of width $\Delta\zeta\propto T$ emerge at the edges

of the light cone in the profiles of generic observables. Such peaks are

described by the same function of $\zeta$ for all local observables.