Exploring Multi-Component Anyons in 1D Optical Lattices: Statistical Phase Sensitivity and Novel Many-Body Behaviors

The study of anyons has gained significant attention in the ultracold atom community due to their potential applications in topological quantum computation, quantum metrology, and the exploration of novel many-body phenomena. Recent theoretical proposals (Phys. Rev. Lett. 115, 053002, 2015; Phys. Rev. A 94, 023615, 2016) and experimental advancements (Science 386, 1055, 2024) in the realization of anyons in one-dimensional optical lattices have spurred further interest. Motivated by these developments, we theoretically investigate the properties and potential realizations of multi-component anyons trapped in a one-dimensional optical lattice. Using Hubbard-like models, we examine both the static and dynamic properties of these systems, focusing on how their behavior depends on the statistical phase. Our analysis combines analytical techniques, including the generalized spin-chain model for anyons in addition to the Jordan-Wigner mapped Hubbard models, with numerical methods such as exact diagonalization and density matrix renormalization group (DMRG). We demonstrate that multi-component anyons exhibit novel behaviors and tunable statistical phase sensitivity that are not present in single-component systems. This work advances our understanding of anyons and highlights their potential utility in quantum metrology and computation.