Mathematical methods point to possibility of particles long thought impossible

Amazing stuff! It appears that two similar papers were published on the same day in Nature. See also my blog post here.

"... However, new research ... shows the possibility of particles that are neither bosons nor fermions. Their study ... mathematically demonstrates the potential existence of paraparticles that have long been thought impossible. ..."

"... The researchers focused on excitations, which can be thought of as particles, in condensed matter systems such as magnets to provide a concrete example for how paraparticles can emerge in nature. ...

Using advanced mathematics, such as Lie algebras, Hopf algebras and representation theory, as well as a pictorial method based on something known as tensor network diagrams to better handle equations, ... were able to perform abstract algebraic calculations to develop models of condensed matter systems where paraparticles emerge. ..."

From the 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 dimensions. In principle, a second exception known as parastatistics, which extends outside two dimensions, has been considered but was believed to be physically equivalent to fermions and bosons.

Here we show that non-trivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. These new types of identical particle 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 that 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, in which free paraparticles emerge as quasiparticle excitations, and their exchange statistics can be physically observed and are 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 particle."

Mathematical methods point to possibility of particles long thought impossible

Mathematical methods point to possibility of particles long thought impossible (original news release) "Rice scientists theoretically demonstrate particles other than bosons and fermions"

Particle exchange statistics beyond fermions and bosons (open access)

Extended Data Fig. 1: The 2D exactly solvable spin model on a 7 × 7 lattice with open boundary conditions.