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Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains.

Alvise Bastianello1, Andrea De Luca2

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|July 20, 2019
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Summary
This summary is machine-generated.

We studied quantum spin chains with time-dependent magnetic flux. Depending on anisotropy, dynamics can be reversible or irreversible, with irreversible behavior linked to increased entanglement entropy.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • Investigating non-equilibrium quantum dynamics is crucial for understanding complex systems.
  • Generalized hydrodynamics (GHD) provides a framework for integrable systems.
  • The Heisenberg anisotropic quantum spin-1/2 chain is a fundamental model for studying quantum magnetism.

Purpose of the Study:

  • To derive an exact description of the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin-1/2 chain under a time-dependent magnetic flux.
  • To identify and characterize different dynamical regimes based on system anisotropy.
  • To extend the generalized hydrodynamics framework for irreversible dynamics.

Main Methods:

  • Utilized the integrability of the quantum spin chain for any flux values.
  • Employed the framework of generalized hydrodynamics (GHD) for slowly varying flux.
  • Introduced a maximum entropy production principle to complement GHD in irreversible regimes.
  • Performed numerical simulations to validate theoretical predictions.

Main Results:

  • Derived a time-dependent generalized Gibbs ensemble description for the system's dynamics.
  • Identified two distinct dynamical regimes: reversible for |Δ|>1 and irreversible for |Δ|<1.
  • Observed a dramatic growth of entanglement entropy in the irreversible regime (|Δ|<1).
  • Demonstrated that the standard GHD is insufficient for irreversible dynamics.

Conclusions:

  • The dynamics of the anisotropic spin chain in a time-dependent flux are precisely described by a time-dependent generalized Gibbs ensemble.
  • Anisotropy (Δ) dictates the reversibility of the dynamics, with |Δ|<1 leading to irreversible behavior and increased entanglement.
  • The maximum entropy production principle successfully extends GHD for irreversible quantum dynamics, showing excellent agreement with numerical results.