Arresting classical many-body chaos by kinetic constraints

TL;DR

This paper explores how kinetic constraints can induce a dynamical phase transition in a classical Heisenberg spin chain, leading to localization phenomena where chaos propagation is halted due to frozen spin islands.

Contribution

It demonstrates a novel dynamical phase transition driven by kinetic constraints, revealing how localized phases emerge in classical many-body chaos.

Findings

Identification of a phase transition between delocalized and localized chaos.

Localization caused by frozen spin islands dominating system dynamics.

Classical OTOC propagates ballistically or not at all depending on constraints.

Abstract

We investigate the effect of kinetic constraints on classical many-body chaos in a translationally-invariant Heisenberg spin chain using a classical counterpart of the out-of-time-ordered correlator (OTOC). The strength of the constraint drives a 'dynamical phase transition' separating a delocalised phase, where the classical OTOC propagates ballistically, from a localised phase, where the OTOC does not propagate at all and the entire system freezes. This is unexpected given that all spins configurations are dynamically connected to each other. We show that localisation arises due to the dynamical formation of frozen islands, contiguous segments of spins immobile due to the constraints, dominating over the melting of such islands.