A matrix product solution for a nonequilibrium steady state of an XX chain

Abstract

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from nearest neighbor z-z, are zero.

11 pages

References in corpus (7)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Operator space entanglement entropy in transverse Ising chain
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Relaxation in the XX quantum chain

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