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Slow dynamics and large deviations in classical stochastic Fredkin chains

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

Slow dynamics and large deviations in classical stochastic Fredkin chains Thumbnail


Luke Causer

Austen Lamacraft


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.


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.

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 (APS)
Peer Reviewed Peer Reviewed
Volume 106
Issue 1
Article Number 014128
Public URL
Publisher URL


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