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Slow dynamics and large deviations in classical stochastic Fredkin chains.

Luke Causer1,2, Juan P Garrahan1,2, Austen Lamacraft3

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Summary
This summary is machine-generated.

This study explores a classical stochastic Fredkin model, revealing slow dynamics and phase transitions. Numerical matrix product states (MPSs) accurately computed its large deviations and hierarchical relaxation.

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Area of Science:

  • Statistical Mechanics
  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • The Fredkin spin chain is a quantum model with a ground state phase transition, including one violating the area law.
  • Classical stochastic models with kinetic constraints often exhibit complex dynamics and emergent phenomena.

Purpose of the Study:

  • To investigate the classical stochastic dynamics of the Fredkin model.
  • To analyze equilibrium and dynamical phase transitions in this stochastic system.
  • To generalize the Fredkin model to two dimensions.

Main Methods:

  • Numerical matrix product states (MPSs) were employed to study the stochastic dynamics.
  • Analysis of autocorrelation functions and hierarchical relaxation processes.
  • Computation of dynamical large deviations and trajectory phases.

Main Results:

  • The stochastic Fredkin model exhibits an equilibrium phase transition mirroring the quantum version.
  • Slow dynamics were observed, characterized by power-law decaying correlations and hierarchical relaxation.
  • An active-inactive phase transition and a hierarchy of trajectory phases were identified in the large deviations.

Conclusions:

  • The classical stochastic Fredkin model accurately reflects quantum phase transitions and displays rich dynamical behavior.
  • Numerical MPS techniques are effective for analyzing complex stochastic systems with kinetic constraints.
  • A two-dimensional generalization of the Fredkin model was proposed using constrained dimer coverings.