Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
Abstract
We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech., L05002 (2010)] is extended to arbitrary coupling constants, driving and homogeneous magnetic field. All one, two and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not gaussian. Nevertheless, in the thermodynamic and weak-driving limit it is only weakly correlated and can be described by a matrix product operator ansatz with matrices of fixed dimension 4. A nonequilibrium phase transition at zero dephasing is also discussed. It is suggested that the scaling of the relaxation time with the system size can serve as a signature of a nonequilibrium phase transition.
Cite
@article{arxiv.1011.0998,
title = {Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation},
author = {Marko Znidaric},
journal= {arXiv preprint arXiv:1011.0998},
year = {2011}
}
Comments
11 pages; v.2: minor changes, published version