Degeneracies and Emergent Symmetries in the Anyon-Hubbard Model

We present findings on the spectral properties and emergent symmetries of the Anyon-Hubbard Model (AHM) of N particles on a line and ring. After diagonalizing hamiltonians related to the AHM, we use the group structure of the symmetries to classify degeneracies in the energy spectrum. Surprisingly, we find symmetries in the few-body configuration spaces not present in single particle systems. Finally, we study the energy level statistics to probe for quantum chaos with few body systems with local and non-local interaction terms. We highlight potential extensions to other correlated hopping models, offering a pathway for realizing robust qubits based on the robustness of these symmetry-protected topological states.