Topological Exchange Statistics in One Dimension

TL;DR

This paper introduces an orbifold topological framework for analyzing exchange statistics in one-dimensional systems, revealing new possibilities for anyons and clarifying the origins of fractional statistics.

Contribution

It proposes a novel orbifold topological approach that unifies exchange statistics analysis across dimensions, especially enabling the study of non-abelian anyons in one dimension.

Findings

Predicts non-abelian anyons in 1D systems

Includes path-ambiguous singular points in configuration space

Clarifies the non-topological origin of fractional statistics

Abstract

The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this approach gives only trivial or near trivial exchange statistics in one dimension because two-body coincidences are excluded from configuration space. Instead, we include these path-ambiguous singular points and consider configuration space as an orbifold. This orbifold topological approach allows unified analysis of exchange statistics in any dimension and predicts novel possibilities for anyons in one-dimensional systems, including non-abelian anyons obeying alternate strand groups. These results clarify the non-topological origin of fractional statistics in one-dimensional anyon models.