Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory

Abstract

The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.

arXiv comment19 pages, fix typos

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Cited by in corpus (4)

• Raman evidence for dimerization and Mott collapse in $\alpha$-RuCl${}_3$ under pressures
• Charge carriers with fractional exclusion statistics in cuprates
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Fractional statistics of charge carriers in the one- and two-dimensional t-J model. A hint for the cuprates?