Abstract
A time-dependent density matrix renormalization group method with a matrix productansatz is employed for explicit computation of non-equilibrium steady state densityoperators of several integrable and non-integrable quantum spin chains, which are drivenfar from equilibrium by means of Markovian couplings to external baths at the two ends. Itis argued that even though the time evolution cannot be simulated efficiently due to fastentanglement growth, the steady states in and out of equilibrium can be typicallyaccurately approximated, with the result that chains of length of the order ofn≈100 spins are accessible. Our results are demonstrated by performing explicit simulations ofsteady states and calculations of energy/spin densities/currents in several problems of heatand spin transport in quantum spin chains. A previously conjectured relation betweenquantum chaos and normal transport is re-confirmed with high accuracy for much largersystems.
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