Exact asymptotics of the current in boundary-driven dissipative quantum chains in large external fields

A boundary-driven quantum master equation for a general inhomogeneous (nonintegrable) anisotropic Heisenberg spin-$1/2$ chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field $f$. We present an exact closed form expression for large $f$ asymptotics of the current in the presence of a pure incoherent source and sink dissipation at the boundaries. In application, we demonstrate an arbitrary large current rectification in the presence of the interaction.

Figure 1

Spin current $J$ as a function of gradient $g$ for linear field profile and anisotropy $\Delta =5$ and $\varepsilon =1$ in systems of size $n=4,6,8$ obtained numerically (Num.) and from Eq. (19) (Anal.). The curve at $n=4$ labeled by ${\Delta }_{\text{inh}}$ shows the same comparison for an inhomogeneous chain with parameters given in the text.

Figure 2

Dependence of flux rectification $R$ on system size $n$ for $\Delta >0,\varepsilon =1$ and gradients $g=3\Delta ,5\Delta ,10\Delta$ obtained from Eqs. (20) and (19). Circles correspond to exact numerics for small systems.