Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current

Abstract

The Lindblad dynamics of the XX quantum chain with large random fields $h_j$ (the couplings $J_j$ can be either uniform or random) is considered for boundary-magnetization-drivings acting on the two end-spins. Since each boundary-reservoir tends to impose its own magnetization, we first study the relaxation spectrum in the presence of a single reservoir as a function of the system size via some boundary-strong-disorder renormalization approach. The non-equilibrium-steady-state in the presence of two reservoirs can be then analyzed from the effective renormalized Linbladians associated to the two reservoirs. The magnetization is found to follow a step profile, as found previously in other localized chains. The strong disorder approach allows to compute explicitly the location of the step of the magnetization profile and the corresponding magnetization-current for each disordered sample in terms of the random fields and couplings.

revised version, 18 pages

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• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• Lindbladians with multiple steady states: theory and applications
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study