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We analyzed entanglement in a quantum fermion model. The study reveals distinct entanglement regimes and transitions using a Coulomb gas approach, confirmed by simulations.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The quantum symmetric simple exclusion process models interacting fermions.
  • Entanglement properties are crucial for understanding quantum many-body systems.
  • Rényi entropies quantify entanglement in quantum subsystems.

Purpose of the Study:

  • To investigate the probability distribution of entanglement in the quantum symmetric simple exclusion process.
  • To analytically compute the large-deviation function of Rényi-q entropies for a subsystem.
  • To characterize the behavior of entanglement at late times and in the thermodynamic limit.

Main Methods:

  • Utilizing a Coulomb gas approach derived from random matrix theory.
  • Calculating the large-deviation function of entropy analytically.
  • Performing numerical Monte Carlo simulations to validate analytical results.

Main Results:

  • The entropy distribution exhibits two or three distinct entanglement regimes for q>1, dependent on the subsystem size (ℓ) to particle number (M) ratio.
  • Singularities in the probability density's third derivative indicate transitions between these regimes.
  • These transitions correspond to changes in the Coulomb gas charge density.

Conclusions:

  • The study provides an analytical framework for understanding entanglement distributions in quantum many-body systems.
  • The Coulomb gas method effectively captures complex entanglement behaviors and transitions.
  • Results offer insights into the nature of quantum entanglement in fermionic systems.