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

By Tomaz Prosen, Marko Znidaric. 2008

182 citations recorded by the source corpus.

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≈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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9511a74985dbcc359978c9e4dac14cfcd71a5546

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum trajectories and open many-body quantum systems (2014, methodology): “These studies have also employed matrix product state methods for such calculations [350, 351].”
Time-evolution methods for matrix-product states (2019, methodology): “Combining Heisenberg and Schrödinger picture time evolution In the context of MPS methods, combining Schrödinger and Heisenberg picture[70, 71] time evolution was first proposed in Ref.”
A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains (2012, background): “Precisely the same case of symmetrically boundary driven XXZ chain (3,4) has been discussed in several recent papers [31, 32, 25, 33, 34, 35] and has been shown to exhibit interesting non-equilibrium trasport properties.”