Anomalous relaxation of density waves in a ring-exchange system

TL;DR

This paper investigates the slow relaxation of density waves in a stochastic ring-exchange model, revealing long-lasting memory effects and unconventional transient structures that challenge existing continuum theories.

Contribution

It provides the first detailed numerical analysis of anomalous relaxation in a ring-exchange system, highlighting long-lived density-wave memory and transient structure formation.

Findings

Long-lasting memory of initial density-wave states

Unconventional transient long-range structures

Discrepancy with mean-field continuum predictions

Abstract

We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models