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arXiv · 2210.02947

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

Murod S. Bahovadinov·Wouter Buijsman·Aleksey K. Fedorov·Vladimir Gritsev·Denis V. Kurlov
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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.

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Murod S. Bahovadinov, Wouter Buijsman, Aleksey K. Fedorov, Vladimir Gritsev, Denis V. Kurlov. 2022-10-06. Many-body localization of ${\mathbb Z}_3$ Fock parafermions. https://doi.org/10.1103/physrevb.106.224205

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