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We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix. For spin 1/2 the matrices satisfy the quantum algebra U_q[sl(2)]. For the isotropic Heisenberg chain, coupled at the ends to boundary reservoirs polarized in different directions with twist angle theta, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain N sites. For large N the in-plane steady-state magnetization profiles are harmonic functions with a frequency proportional to the twist angle. In-plane steady-state magnetization currents are subdiffusive, while the transverse current saturates when the coupling strength is sufficiently large. For the anisotropic chain we find a current resonance at the specific values of the anisotropic interaction strength where the transverse current is independent of system size, even for non-integrable higher-spin chains.

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Gunter Schütz, FZ Jülich
TP seminar room 0.03
Contact: Joachim Krug