Anyon-Induced Criticality and Dynamical Stability in Non-Hermitian Many-Body Systems

TL;DR

This paper demonstrates that anyonic statistics induce a unique non-Hermitian critical transition characterized by dense spectra and enhanced stability, fundamentally altering the spectral properties and dynamical behavior of many-body systems.

Contribution

It reveals that anyonic exchange statistics intrinsically cause non-Hermitian criticality and spectral transitions, even when bosonic and pseudofermionic systems do not exhibit such features.

Findings

Anyonic statistics break pseudo-Hermiticity and induce real-complex spectral transitions.

The spectrum shows dense states in the imaginary part of energy, indicating non-Hermitian criticality.

Enhanced spectral gaps lead to stable short-time dynamics for anyons.

Abstract

We show that anyonic statistics fundamentally reshapes non-Hermitian many-body physics by intrinsically breaking pseudo-Hermiticity, leading to a unique real-complex spectral transition with characteristically dense states in Im$E$. This anyon-induced transition occurs even when bosonic and pseudofermionic counterparts remain entirely real, revealing a form of non-Hermitian criticality driven purely by exchange statistics. The resulting spectrum exhibits enhanced gaps in Im$E$ that dynamically isolate dominant eigenstates, producing anomalously stable short-time quench dynamics for anyons. Our results identify anyonic statistics as an intrinsic mechanism for generating unconventional non-Hermitian critical behavior usually associated with highly non-local systems.