Slow dynamics and large deviations in classical stochastic Fredkin chains

Causer, Luke; Garrahan, Juan P.; Lamacraft, Austen

Abstract

The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations - which we compute accurately via numerical MPSs - including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.

Citation

Causer, L., Garrahan, J. P., & Lamacraft, A. (2022). Slow dynamics and large deviations in classical stochastic Fredkin chains. Physical Review E, 106(1), Article 014128. https://doi.org/10.1103/PhysRevE.106.014128

• Journal Article Type: Article
• Acceptance Date: Jul 5, 2022
• Online Publication Date: Jul 21, 2022
• Publication Date: Jul 1, 2022
• Deposit Date: Jul 25, 2022
• Publicly Available Date: Jul 25, 2022
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 106
• Issue: 1
• Article Number: 014128
• DOI: https://doi.org/10.1103/PhysRevE.106.014128
• Public URL: https://nottingham-repository.worktribe.com/output/9400281
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.014128