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captures ground-state properties of the full Anyon--Hubbard model reported in S.~Basak, X.-W.~Guan, and H.~Pu, unpublished manuscript (2026), and reveals that their statistical dependence is predominantly encoded in the explicit anyonic structure of the observables rather than the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.