Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport

Abstract

Explicit matrix product ansatz is presented, in first two orders in the (weak) coupling parameter, for the non-equilibrium 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 thermodynamic limit an exact pseudo-local conservation law and yields -- via Mazur inequality -- a rigorous lower bound on the high temperature spin Drude weight. Such Mazur bound is a non-vanishing fractal function of the anisotropy parameter Delta for |Delta|<1.

Slightly longer but essentially equivalent to a published version

References in corpus (5)

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Cited by in corpus (10)

• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Spin transport in a one-dimensional anisotropic Heisenberg model
• PT-symmetric quantum Liouvillian dynamics
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• The Luttinger liquid and integrable models
• Decay of currents for strong interactions
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes