Nonequilibrium steady states in the quantum XXZ spin chain
Résumé
We investigate the real-time dynamics of a critical spin-1/2 chain (XXZ model) prepared in an inhomogeneous initial state with different magnetizations on the left and right halves. Using the time-evolving block decimation method, we follow the front propagation by measuring the magnetization and entanglement entropy profiles. At long times, as in the free fermion case [Antal et al., Phys. Rev. E 59, 4912 (1999)], a large central region develops where correlations become time independent and translation invariant. The shape and speed of the fronts is studied numerically and we evaluate the stationary current as a function of initial magnetic field and as a function of the anisotropy Δ . We compare the results with the conductance of a Tomonaga-Luttinger liquid, and with the exact free-fermion solution at Δ=0 . We also investigate the two-point correlations in the stationary region and find a good agreement with the “twisted” form obtained by Lancaster and Mitra [Phys. Rev. E 81, 061134 (2010)] using bosonization. Some deviations are nevertheless observed for strong currents.