Integrable quantum dynamics of open collective spin models

TL;DR

This paper presents an exact solution for the spectral properties of a collective quantum spin system interacting with Markovian baths, revealing phase transitions and decay behaviors in the large-spin limit.

Contribution

It introduces a method to find integrable Liouvillian operators with non-trivial steady states using a conserved super-operator charge and differential representation.

Findings

Spectral density diverges along certain complex plane curves.

Characterization of steady states at phase transitions.

Determination of decay rates for coherences and populations.

Abstract

We consider a collective quantum spin-$s$ in contact with Markovian spin-polarized baths. Using a conserved super-operator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigen-modes. We study the spectral properties of the model in the large-$s$ limit using a semi-classical quantization condition and show that the spectral density may diverge along certain curves in the complex plane. We exploit our exact solution to characterize steady-state properties, in particular at the discontinuous phase transition that arises for unpolarized environments, and to determine the decay rates of coherences and populations. Our approach provides a systematic way of finding integrable Liouvillian operators with non-trivial steady-states as well as a way to study their spectral properties and eigen-modes.