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Noncommuting conserved charges in quantum many-body thermalization.

Nicole Yunger Halpern1,2,3,4, Michael E Beverland5, Amir Kalev6

  • 1Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review. E
|May 20, 2020
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Summary
This summary is machine-generated.

Researchers propose an experimental method to observe systems reaching a non-Abelian thermal state (NATS) by relaxing noncommuting conserved quantities. This quantum thermodynamics advance moves beyond traditional assumptions for finite systems.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Quantum Many-Body Physics

Background:

  • In statistical mechanics, systems typically exchange conserved quantities (heat, particles) with a bath, reaching canonical or grand canonical ensembles.
  • A recent quantum-information-theoretic (QI-theoretic) approach relaxes the assumption that conserved quantity operators must commute.
  • This leads to the concept of a non-Abelian thermal state (NATS) for the small system's long-time state.

Purpose of the Study:

  • To propose a feasible experimental protocol for observing a system thermalize to the NATS.
  • To extend the NATS theory from abstract idealizations to realistic finite systems with finite couplings and times.
  • To introduce noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics.

Main Methods:

  • Theoretical analysis of a spin chain model where a subset acts as the system and the rest as an effective bath.
  • Heisenberg interactions are used to model the exchange of conserved quantities (spin components) between the system and bath.
  • Numerical simulations are employed to support analytical predictions of long-time expectation values.

Main Results:

  • Analytical predictions for long-time expectation values in finite systems thermalizing with finite couplings.
  • Numerical simulations confirm that the system thermalizes to a state near the NATS.
  • The observed thermalization deviates from the predictions of the standard canonical ensemble.

Conclusions:

  • The proposed experimental protocol provides a pathway to observe NATS in realistic quantum systems.
  • The study validates the NATS theory for finite systems, bridging theoretical concepts with practical implementations.
  • The findings have implications for atomic, molecular, and optical physics, condensed matter physics, and quantum information science.