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

Cécile Monthus (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Keywords: transport properties; quantum dissipative systems; disordered spin chains; current fluctuations

Domains: Physics [physics]

Cécile Monthus. Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current. Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017, pp.043303. ⟨10.1088/1742-5468/aa6a2f⟩. ⟨cea-01472970⟩