Parastatistics revealed: Peierls phase twists and shifted conformal towers in interacting periodic chains

TL;DR

This paper investigates interacting paraparticle chains with a constant R-matrix, revealing how their spectra and conformal towers are affected by boundary conditions, flux sectors, and parastatistics, with exact solutions in certain regimes.

Contribution

It demonstrates a general factorization of the Hilbert space for flavor-blind Hamiltonians and shows how parastatistics manifest in the energy spectrum through flux sectors and conformal towers.

Findings

Spectrum coincides with occupation Hamiltonian for open boundaries.

Periodic boundaries lead to flux sectors revealing parastatistics.

Exact solutions show flux-shifted conformal towers and temperature-dependent chemical potential.

Abstract

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.