Emergent parastatistical quasiparticles in exactly solvable lattice spin models

Parastatistics is one of the few alternatives to the usual fermion and boson statistics. Parastatistical particles transform in higher dimensional representations of the permutation group under particle exchange, and satisfy generalized Pauli exclusion principles. While their existence as elementary particles has been ruled out by a no-go theorem [1] in relativistic quantum field theory, in this talk I show that they can emerge as emergent quasiparticles in a family of parity-time-symmetric quantum lattice spin models. This family of models can be exactly solved using a generalized Jordan-Wigner transformation, which transforms the spin operators into paraparticle creation and annihilation operators satisfying generalized quadratic commutation relations. (Note: This is very different from the notion of parafermions [2], which don’t form higher dimensional representation of the permutation group.) The single particle spectra are the same as certain lattice free fermion systems, but the paraparticles satisfy generalized Pauli exclusion principles, i.e. the same state can hold up to n paraparticles, where n is a constant integer. The models can exhibit several interesting phase transitions, including a band insulator-conductor- topological insulator transition, where the critical exponents can be exactly calculated.

References:

[1] S. Doplicher, R. Haag, and J.E. Roberts, Commun. Math. Phys. 23, 199–230 (1971); Commun. Math. Phys. 35, 49–85 (1974)

[2] P. Fendley, J. Stat. Mech. P11020 (2012)