Abstract
We study nonequilibrium quantum phase transitions in the XY spin 1/2 chain using the 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 , 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 algebra. We also study the thermalization properties of the mesoreservoir approach.
Highlights
Equilibrium phase transitions are determined as non-analyticities of the free energy and can strictly appear only in the thermodynamic limit [1]
We studied nonequilibrium quantum phase transitions in the XY spin 1/2 chain analytically using the C∗ algebra method
We showed that the quantum phase transitions (QPT) at h = 1 is present in nonequilibrium if one temperature of the reservoirs remains at absolute zero
Summary
Equilibrium phase transitions are determined as non-analyticities of the free energy and can strictly appear only in the thermodynamic limit [1]. Since all real parts of the correlation matrix have this property, a genuine NQPT should be discussed through Im fl†fm , which vanishes for equilibrium state (The kernel is proportional to the difference of Fermi distributions calculated with the initial temperatures of the left and right semi-infinite parts.). At γ = 0 and h = hc = 1 we find a square root divergence of magnetic susceptibility with the temperature TL,R and the difference of magnetic field from one |1 − h|, namely χ(γ = 0, h, TL/R = 0) ∝ |1 − h|−1/2, χ(γ = 0, h = 1, TL/R) ∝ TL−/1R/2 In this case (γ = 0, h = 1), the finite temperature nonequilibrium transitions associated to discontinuities in the derivatives of the imaginary parts of the correlation functions disappear. The existence of NESS guarantees that the equation (16) has a solution, which can be computed efficiently in O(N 3) steps
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