English

Parafermionic Truncated Wigner Approximation

Strongly Correlated Electrons 2026-04-01 v1

Abstract

We introduce the parafermionic truncated Wigner approximation (ppTWA), a semiclassical phase-space framework for simulating the nonequilibrium dynamics of lattice systems with fractional exchange statistics. The method extends truncated Wigner approaches developed for bosonic and fermionic systems to Zn\mathbb{Z}_n Fock parafermions by expressing the Hamiltonian in terms of local Hubbard operators that form a closed Lie algebra. This representation leads to a Lie--Poisson phase-space formulation in which quantum dynamics is approximated by stochastic sampling of initial conditions followed by deterministic semiclassical evolution. We benchmark the approach in several settings, including single-site clock dynamics, the fully connected Zn\mathbb{Z}_n clock model, long-range Z3\mathbb{Z}_3 clock chains, and disordered Z3\mathbb{Z}_3 Fock parafermion chains. The method reproduces key features of the exact dynamics, including excitation spreading, disorder-induced suppression of transport, and the emergence of long-time imbalance plateaus. Our results demonstrate that ppTWA provides a practical tool for exploring the dynamics of parafermionic systems in regimes where exact numerical methods are limited by Hilbert-space growth.

Keywords

Cite

@article{arxiv.2603.29344,
  title  = {Parafermionic Truncated Wigner Approximation},
  author = {Javad Vahedi and Martin Garttner},
  journal= {arXiv preprint arXiv:2603.29344},
  year   = {2026}
}

Comments

16 pages, 6 figures

R2 v1 2026-07-01T11:45:37.567Z