"Numerics for an XXZ spin chain out of equilibrium - revisiting Antal's quench"
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We investigate the dynamics of a critical XXZ spin-1/2 chain prepared in an
inhomogeneous initial state with different magnetizations on the left and right
halves. We simulate the real-time evolution using the time-evolving block
decimation (TEBD) method. We follow the front propagation by measuring the
magnetization and entanglement entropy profiles, and we focus on the situation
where the initial state is not fully polarized. At long times, as in the free
fermion case (T. Antal et al. 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 \Delta. We compare the results with the conductance of a
Tomonaga-Luttinger liquid, and with the exact free-fermion solution at \Delta=0.
We also investigate the two-point correlations in the stationary region and find
a good agreement with the "twisted" form obtained by J. Lancaster and A. Mitra
(2010) using bosonization. Some deviations are nevertheless observed for strong
currents.