Slow dynamics and large deviations in classical stochastic Fredkin chains

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

Automated summary

The Fredkin spin chain is an interesting theoretical model that exhibits a ground-state phase transition between distinct phases, one of which violates the area law. In this study, we analyze the classical stochastic dynamics of a stochastic version of the Fredkin model, which is a simple exclusion process subject to additional kinetic constraints. We find that the equilibrium phase transition in the stochastic problem parallels the ground-state phase transition of the quantum chain, and we quantify its properties using 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.