A note on the topological order of noncommutative Hall fluids

TL;DR

This paper investigates the topological order of noncommutative Hall fluids by evaluating ground state degeneracy in noncommutative Chern-Simons models, introducing a family of generalized models via T-duality.

Contribution

It defines a new class of noncommutative, non-abelian fluid models and computes their topological order, extending the understanding of Hall fluid phases.

Findings

Ground state degeneracy evaluated for noncommutative Chern-Simons models.

Proposed a discrete family of noncommutative, non-abelian fluid models.

Computed topological order for these models.

Abstract

We evaluate the ground state degeneracy of noncommutative Chern-Simons models on the two-torus, a quantity that is interpreted as the "topological order" of associated phases of Hall fluids. We define the noncommutative theory via T-duality from an ordinary Chern-Simons model with non-abelian 't Hooft magnetic fluxes. Motivated by this T-duality, we propose a discrete family of noncommutative, non-abelian fluid models, arising as a natural generalization of the standard noncommutative Chern-Simons effective models. We compute the topological order for these universality classes, and comment on their possible microscopic interpretation.