Statistics-governed dynamical scaling in interacting anyonic chains

TL;DR

This paper reveals that anyonic statistics induce unique, universal dynamical scaling behaviors in one-dimensional quantum systems far from equilibrium, differing from traditional Bose-Fermi dynamics, with implications for quantum simulations.

Contribution

It demonstrates that anyonic statistics lead to emergent superdiffusive transport and ballistic entanglement growth, establishing a new class of nonequilibrium dynamics beyond bosons and fermions.

Findings

Anyonic statistics cause superdiffusive particle transport.

Entanglement entropy remains ballistic regardless of statistics.

Statistics-induced quantum interference suppresses holon-doublon propagation.

Abstract

Particle statistics impose fundamental constraints on nonequilibrium quantum dynamics, yet it remains an open question whether anyonic statistics can lead to emergent dynamical scaling beyond the conventional Bose-Fermi paradigm. Here we investigate the far-from-equilibrium many-body relaxation of anyons in a one-dimensional lattice, uncovering a statistics-governed, robust scaling behavior that deviates from standard Bose-Fermi limits. Based on large-scale numerical simulations and scaling analysis, we find that in the weakly interacting regime, anyonic statistics leads to emergent superdiffusive scaling in particle transport, while the entanglement entropy remains ballistic and is essentially insensitive to exchange statistics. The anomalous dynamics can be interpreted intuitively from the statistical-phase-induced quantum interference that suppresses coherent holon-doublon propagation; in contrast, the entanglement growth is dominated by its configurational component, which maintains ballistic spreading regardless of the statistical phase. Our results establish anyonic statistics as a distinct source of universal nonequilibrium dynamics beyond bosons and fermions, with direct relevance to current quantum simulation experiments.