All known particles are fermions or bosons. While exceptions are known in 2D space (anyons), fermions and bosons were widely believed to be the only possibilities in 3D.

In this talk, I will describe our results [Wang & Hazzard, Nature 637, 314 (2025)] showing it is possible to have particles that are inequivalent to fermions and bosons, known as paraparticles, in arbitrary dimension. I will describe how these emerge as excitations in solvable spin models. These constructions satisfy all known physical principles required of a quantum theory, including the principle of locality, i.e. that disturbing a system at some point in space does not instantaneously affect far away points. This is crucial, as powerful theorems of algebraic quantum field theory show that locality constrains particle statistics, which presented an obstacle to previous theories of paraparticles. I will describe how our construction evades these theorems' constraints, some implications, and experimental systems in ultracold matter where we may begin to search for paraparticles.