Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation

We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation...

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Bibliographic Details
Published in:Physical review. B 2020-09, Vol.102 (9), p.1, Article 094430
Main Authors: Louw, Jan C., Kastner, Michael, Kriel, Johannes N.
Format: Article
Language:English
Subjects:
Eigenvalues
Eigenvectors
Exact solutions
Mathematical analysis
Perturbation theory
Representations
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Summary:We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.102.094430