Spin, Statistics and Charge of Solitons in (2+1)-Dimensional Theories

TL;DR

This paper derives universal formulas for the quantum numbers of solitons in (2+1)D models, revealing their fermionic or bosonic nature and charge, with implications for topological quantum states.

Contribution

It provides general topologically invariant expressions for soliton quantum numbers in (2+1)D models, clarifying their spin and charge properties.

Findings

Solitons can be fermions with half-integer spin and odd charge.

Solitons can be bosons with integer spin and even charge.

Results are exemplified in a lattice model related to high-Tc superconductors.

Abstract

General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or integer spin bosons with even charge. So they cannot be Anderson's spinons or holons. General results are exemplified by a square lattice model reminiscenting high-Tc models.