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Integrable Quantum Dynamics of Open Collective Spin Models.

Pedro Ribeiro1,2, Tomaž Prosen3

  • 1CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal.

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We present an exact solution for quantum spin systems interacting with spin-polarized baths. This method reveals spectral properties and characterizes phase transitions and decay rates in quantum systems.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Investigating quantum spin systems interacting with external environments is crucial for understanding complex quantum phenomena.
  • Markovian spin-polarized baths are common models for open quantum systems.

Purpose of the Study:

  • To develop an exact method for solving the spectral properties of collective quantum spin systems in contact with Markovian baths.
  • To characterize the steady-state properties and phase transitions of these systems.

Main Methods:

  • Construction of a differential representation of the Liouvillian using a conserved superoperator charge.
  • Application of a semiclassical quantization condition for analyzing the large-s limit.
  • Exact solution to determine spectral properties, steady states, and decay rates.

Main Results:

  • The exact spectrum and eigenmodes of the Liouvillian were determined.
  • Spectral density was shown to diverge along specific curves in the complex plane in the large-s limit.
  • Steady-state properties, including behavior at a discontinuous phase transition, were characterized.

Conclusions:

  • The developed approach offers a systematic way to find integrable Liouvillian operators with nontrivial steady states.
  • This method enables the study of spectral properties and eigenmodes in open quantum spin systems.