Paired quantum Hall states on noncommutative two-tori

Abstract

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings ν = m p m + 2 Cristofano et al. (2000) [1], recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) [2] for the Jain series ν = m 2 p m + 1 . The case m = 2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.