An explicit matrix product ansatz is presented, in the first two orders in the (weak) coupling parameter, for the nonequilibrium steady state of the homogeneous, nearest neighbor Heisenberg XXZ spin 1/2 chain driven by Lindblad operators which act only at the edges of the chain. The first order of the density operator becomes in the thermodynamic limit an exact pseudolocal conservation law and yields -- via the Mazur inequality -- a rigorous lower bound on the high-temperature spin Drude weight. Such a Mazur bound is found a nonvanishing fractal (nowhere smooth) function of the anisotropy parameter Delta for Delta|(1.

COBISS.SI-ID: 2347108

Using a combination of numerical and analytical methods we have classified transport in the XXZ model for all values of the anisotropy. For large anisotropies the diffusion constant scales inversely with the anisotropy. At the isotropic point an anomalous transport is demnonstrated, being a first example of anomalous transport in a coherent quantum model.

COBISS.SI-ID: 2357860

We study real-time dynamics of a charge carrier introduced into an undoped Mott insulator propagating under a constant electric field F on the t-J ladder and a square lattice. We calculate the quasistationary current. In both systems an adiabatic regime is observed followed by a positive differential resistivity (PDR) at moderate fields where the carrier mobility is determined. Quantitative differences between the ladder and two-dimensional (2D) systems emerge when at large fields both systems enter the negative differential resistivity (NDR) regime. In the ladder system Bloch-like oscillations prevail, while in two dimensions the current remains finite, proportional to 1/F. The crossover between the PDR and NDR in two dimensions is accompanied by a change of the spatial structure of the propagating spin polaron.

COBISS.SI-ID: 24707879