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

TL;DR

This paper uses matrix product methods to efficiently compute non-equilibrium steady states in quantum spin chains, enabling analysis of large systems and confirming links between quantum chaos and transport properties.

Contribution

Introduces a matrix product density operator approach to simulate large non-equilibrium quantum spin chains and verify theoretical conjectures.

Findings

Steady states can be accurately approximated for chains of length ~100.

Confirmed relation between quantum chaos and normal transport.

Demonstrated heat and spin transport properties in large quantum chains.

Abstract

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 can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 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. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.