Matrix product simulations of non-equilibrium steady states of quantum spin chains

A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time evolution cannot be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, with the result that chains of length of the order of n approximate to 100 spins are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. A previously conjectured relation between quantum chaos and normal transport is re-confirmed with high accuracy for much larger systems.