Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain

TL;DR

This paper provides an explicit analytical solution for the 2-point correlation function in a boundary-driven XY spin chain, revealing a quantum phase transition and novel correlation resonances in non-equilibrium steady states.

Contribution

It offers the first explicit solution for the correlation functions in this model and uncovers a new quantum phase transition and resonance phenomena.

Findings

Identification of a quantum phase transition from exponential decay to long-range order.

Discovery of correlation resonances at specific external parameter values.

Analytical characterization of the non-equilibrium steady state.

Abstract

Explicit solution for the 2-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long-range order is discussed analytically. In the regime of long-range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for certain discrete values of the external bulk parameter, e.g. the magnetic field.