Many-body localization of ${\mathbb Z}_3$ Fock parafermions

TL;DR

This paper demonstrates that ${ m Z}_3$ Fock parafermions, which are exotic anyonic quasiparticles, can undergo a many-body localization transition in a disordered 1D system, contrasting with conventional quadratic disordered Hamiltonians.

Contribution

It establishes a link between a disordered spin chain and a ${ m Z}_3$ parafermion model, showing MBL transition due to nontrivial statistics despite quadratic form.

Findings

Evidence of MBL transition from level-spacing statistics

Finite-size scaling of entanglement entropy supports MBL

Fractal dimensions indicate localized phase

Abstract

We study the effects of a random magnetic field on a one-dimensional (1D) spin-1 chain with {\it correlated} nearest-neighbor $XY$ interaction. We show that this spin model can be exactly mapped onto the 1D disordered tight-binding model of ${\mathbb Z}_3$ Fock parafermions (FPFs), exotic anyonic quasiparticles that generalize usual spinless fermions. Thus, we have a peculiar case of a disordered Hamiltonian that, despite being bilinear in the creation and annihilation operators, exhibits a many-body localization (MBL) transition owing to the nontrivial statistics of FPFs. This is in sharp contrast to conventional bosonic and fermionic quadratic disordered Hamiltonians that show single-particle (Anderson) localization. We perform finite-size exact diagonalization calculations of level-spacing statistics, fractal dimensions, and entanglement entropy, and provide convincing evidence for the MBL transition at finite disorder strength.