Parastatistics in Interacting Periodic Chains Revealed by Peierls Phase Twists and Shifted Conformal Towers
We consider interacting paraparticle chains with a constant $R$-matrix where the Hamiltonian sums over the internal degrees (flavors) of the paraparticles. For such flavor-blind Hamiltonians we show a general factorization of the Hilbert space into occupation and flavor parts with the Hamiltonian acting non-trivially only on the former. For open boundaries, the spectrum therefore coincides with that of the occupation Hamiltonian $H_{\rm occ}$ with the flavor part merely adding degeneracies. For periodic boundaries, a cyclic reordering of the flavors leads to a separation of $H_{\rm occ}$ into flux sectors at fixed particle number, thus making the parastatistics directly observable in the energy spectrum. For important exemplary cases, $H_{\rm occ}$ reduces to the XXZ chain with flux allowing for an exact solution. In the gapless regime, this solution shows flux-shifted $c=1$ conformal towers in the low-energy spectrum and a temperature-dependent chemical potential in the bulk thermodynamics.