Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown

TL;DR

This paper studies the annealing dynamics of classical rotor networks, revealing universal scaling behaviors and their breakdown with increasing interaction range, contrasting quantum and classical systems.

Contribution

It identifies universal features and their breakdown in the annealing dynamics of classical rotor networks with varying interaction ranges and topologies.

Findings

Universal Kibble-Zurek scaling in low-connectance graphs

Suppression of power-law scaling with increased interaction range

Exponential scaling emerges in long-range interaction regimes

Abstract

The spin-vector Monte Carlo model is widely used as a benchmark for the classicality of quantum annealers but severely restricts the time evolution. The spin-vector Langevin (SVL) model has been proposed and tested as an alternative, closely reproducing the real-time dynamics of physical quantum annealers such as D-Wave machines in the dissipative regime. We investigate the SVL annealing dynamics of classical O(2) rotors on regular graphs, identifying universal features in the nonequilibrium dynamics when changing the range of interactions and the topology of the graph. Regular graphs with low connectance or edge density exhibit universal scaling dynamics consistent with the Kibble-Zurek mechanism, which leads to a power-law dependence of the density of defects and the residual energy as a function of the annealing time. As the interaction range is increased, the power-law scaling is suppressed, and an exponential scaling with the annealing time sets in. Our results establish a universal breakdown of the Kibble-Zurek mechanism in classical systems characterized by long-range interactions, in sharp contrast with previous findings in the quantum domain.