Entanglement and Transport Properties of Non-Equilibrium Steady States of 1-D Quantum Systems

We numerically study the non-equilibrium steady states of two 1-D models, a free fermion quantum wire model and a Heisenberg XXZ chain, both governed by open system Linblad dynamics. The physical setup consists of a unitarily evolving "bulk" coupled via its boundaries to two dissipative "leads".

For the quantum wire, the open system dynamics is designed to drive the leads to thermal equilibrium, and by choosing different temperatures and chemical potentials for the two leads we may drive the bulk into a non-equilibrium current carrying steady state. We report two main results in this context. First, we show that for an appropriate choice of dynamics of the leads, the bulk state is also driven to thermal equilibrium even though the open system dynamics does not act directly on it. Second, we show that the steady state which emerges at later time, even in the presence of currents, is lightly entangled in the sense of having small mutual information and conditional mutual information for appropriate regions. We also report results for the rate of approach to the steady state.

For the Heisenberg model, the leads impose fixed magnetizations at the ends of the chain, and can be tuned to enforce a spin density gradient across the chain. We use the matrix product formalism to study the transport properties of this model in two qualitatively different regimes: ideal conductor and diffusive conductor. We show numerically that matrix product states are a good approximation for the steady states of this model.

More generally, our work has bearing on recent attempts to formulate numerically tractable methods to compute transport properties in strongly interacting models.