Generalized Effective Spin-Chain formalism for multicomponent anyons in one-dimensional optical lattices
Abstract
We develop a generalized effective spin-chain (GESC) formalism for strongly interacting multicomponent anyons in a one-dimensional (1D) optical lattice. By mapping particle motion onto spinless fermions and spin states onto an ordered chain, this framework provides a spin--charge-separated perspective on the physical effects of fractional exchange statistics. In the strong-interaction regime, the leading-order charge Hamiltonian becomes independent of the statistical phase; instead, virtual tunneling through doubly occupied states directly imprints this phase on the spin-exchange coefficients. The GESC formalism captures ground-state properties of the full Anyon--Hubbard model reported in S.~Basak, X.-W.~Guan, and H.~Pu, unpublished manuscript (2026), and reveals that their statistical dependence is predominantly encoded in the explicit anyonic structure of the observables rather than the underlying spin ground state. This formalism uncovers that, out of equilibrium, successive spin exchanges accumulate direction-dependent phases; the resulting interference drives crossover from dispersive to localized impurity transport and generates inversion-asymmetric propagation at intermediate statistics. Suppressed expansion persists for identical and distinguishable impurities, with differences in propagation governed by the interplay between impurity identity and interaction anisotropy. Ultimately, GESC offers a versatile, computationally efficient theoretical framework that connects macroscopic dynamics to microscopic virtual exchange processes, conferring a unique spin--charge-separated vantage for resolving how fractional exchange statistics survives strong interactions and manifests distinctly across static and dynamical regimes.
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BibTeX
@misc{basak2026generalized,
title = {{Generalized Effective Spin-Chain formalism for multicomponent anyons in one-dimensional optical lattices}},
author = {Sagarika Basak and Xi-Wen Guan and Han Pu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36555},
eprint = {2609.36555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36555},
}
RIS
TY - UNPB
TI - Generalized Effective Spin-Chain formalism for multicomponent anyons in one-dimensional optical lattices
AU - Sagarika Basak
AU - Xi-Wen Guan
AU - Han Pu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36555
UR - https://arxiv.org/abs/2609.36555
AB - We develop a generalized effective spin-chain (GESC) formalism for strongly interacting multicomponent anyons in a one-dimensional (1D) optical lattice. By mapping particle motion onto spinless fermions and spin states onto an ordered chain, this framework provides a spin--charge-separated perspective on the physical effects of fractional exchange statistics. In the strong-interaction regime, the leading-order charge Hamiltonian becomes independent of the statistical phase; instead, virtual tunneling through doubly occupied states directly imprints this phase on the spin-exchange coefficients. The GESC formalism captures ground-state properties of the full Anyon--Hubbard model reported in S.~Basak, X.-W.~Guan, and H.~Pu, unpublished manuscript (2026), and reveals that their statistical dependence is predominantly encoded in the explicit anyonic structure of the observables rather than the underlying spin ground state. This formalism uncovers that, out of equilibrium, successive spin exchanges accumulate direction-dependent phases; the resulting interference drives crossover from dispersive to localized impurity transport and generates inversion-asymmetric propagation at intermediate statistics. Suppressed expansion persists for identical and distinguishable impurities, with differences in propagation governed by the interplay between impurity identity and interaction anisotropy. Ultimately, GESC offers a versatile, computationally efficient theoretical framework that connects macroscopic dynamics to microscopic virtual exchange processes, conferring a unique spin--charge-separated vantage for resolving how fractional exchange statistics survives strong interactions and manifests distinctly across static and dynamical regimes.
ER -