Particle exchange statistics beyond fermions and bosons

Abstract: It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension. In principle, a second exception known as parastatistics, which extends outside of two dimensions, has been considered but was believed to be physically equivalent to fermions and bosons. In this paper we show that nontrivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. These new types of identical particles obey generalized exclusion principles, leading to exotic free-particle thermodynamics distinct from any system of free fermions and bosons. We formulate our theory by developing a second quantization of paraparticles, which naturally includes exactly solvable non-interacting theories, and incorporates physical constraints such as locality. We then construct a family of exactly solvable quantum spin models in one and two dimensions where free paraparticles emerge as quasiparticle excitations, and their exchange statistics can be physically observed and is notably distinct from fermions and bosons. This demonstrates the possibility of a new type of quasiparticle in condensed matter systems, and, more speculatively, the potential for previously unconsidered types of elementary particles.