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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.29344 |
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| _version_ | 1866910088314224640 |
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| author | Vahedi, Javad Garttner, Martin |
| author_facet | Vahedi, Javad Garttner, Martin |
| contents | We introduce the parafermionic truncated Wigner approximation ($p$TWA), 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 $\mathbb{Z}_n$ 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 $\mathbb{Z}_n$ clock model, long-range $\mathbb{Z}_3$ clock chains, and disordered $\mathbb{Z}_3$ 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 $p$TWA provides a practical tool for exploring the dynamics of parafermionic systems in regimes where exact numerical methods are limited by Hilbert-space growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parafermionic Truncated Wigner Approximation Vahedi, Javad Garttner, Martin Strongly Correlated Electrons We introduce the parafermionic truncated Wigner approximation ($p$TWA), 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 $\mathbb{Z}_n$ 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 $\mathbb{Z}_n$ clock model, long-range $\mathbb{Z}_3$ clock chains, and disordered $\mathbb{Z}_3$ 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 $p$TWA provides a practical tool for exploring the dynamics of parafermionic systems in regimes where exact numerical methods are limited by Hilbert-space growth. |
| title | Parafermionic Truncated Wigner Approximation |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.29344 |