Nonequilibrium quantum phase transitions in the XY model: comparison of unitary time evolution and reduced density operator approaches

Abstract

We study nonequilibrium quantum phase transitions in the XY spin 1/2 chain using the ${{C}^{*}}$ algebra. We show that the well-known quantum phase transition at a magnetic field of h = 1 also persists in the nonequilibrium setting as long as one of the reservoirs is set to absolute zero temperature. In addition, we find nonequilibrium phase transitions associated with an imaginary part of the correlation matrix for any two different reservoir temperatures at h = 1 and $h={{h}_{\text{c}}}\left| 1-{{\gamma }^{2}} \right|$ , where γ is the anisotropy and h the magnetic field strength. In particular, two nonequilibrium quantum phase transitions coexist at h = 1. In addition, we study the quantum mutual information in all regimes and find a logarithmic correction of the area law in the nonequilibrium steady state independent of the system parameters. We use these nonequilibrium phase transitions to test the utility of two models of a reduced density operator, namely the Lindblad mesoreservoir and the modified Redfield equation. We show that the nonequilibrium quantum phase transition at h = 1, related to the divergence of magnetic susceptibility, is recovered in the mesoreservoir approach, whereas it is not recovered using the Redfield master equation formalism. However, none of the reduced density operator approaches could recover all the transitions observed by the ${{C}^{*}}$ algebra. We also study the thermalization properties of the mesoreservoir approach.

Keywords

• nonequilibrium quantum phase transition
• XY model
• quantum spin chain
• exact solution
• 03.65.Fd
• 05.70.Ln