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Parastatistics in interacting periodic chains revealed by Peierls phase twists
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We review various concepts of quantum statistics beyond simple bosons and
fermions, including anyons, parafermions and Fock parafermions and Haldane’s exclusion
statistics. We then discuss the of R-paraparticles recently introduced by Wang and Hazzard
(Nature, 2025). Here we consider interacting paraparticle chains with a constant R matrix
where the Hamiltonian sums over the internal degrees (flavours) of the paraparticles.
For such flavour-blind Hamiltonians, we show a general factorisation of the Hilbert space into
occupation and flavour parts with the Hamiltonian acting nontrivially only on the former.
For open boundaries, the spectrum therefore coincides with that of the occupation
Hamiltonian with the flavour part merely adding degeneracies. For periodic boundaries, a
cyclic reordering of the flavours leads to a separation of the occupation Hamiltonian into flux
sectors at fixed particle number, thus making the parastatistics directly observable in the
energy spectrum. For important exemplary cases, the occupation Hamiltonian reduces to the
XXZ chain with flux, allowing for an exact solution.
SFB 1277 · Seminar
2D van der Waals Josephson devices
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