Paired states on a torus

TL;DR

This paper investigates the modular properties of the conformal field theory describing paired quantum Hall states at filling nu=1/(p+1), revealing connections to orbifold constructions and the Moore-Read state.

Contribution

It constructs the characters and partition functions for these states, clarifies their orbifold structure, and links tunneling phenomena to the Moore-Read model.

Findings

Partition functions for twisted and untwisted sectors are constructed.

The state exhibits a Z_2-orbifold structure in its CFT description.

Tunneling processes select a twist-invariant CFT matching the Moore-Read state.

Abstract

We analyze the modular properties of the effective CFT description for paired states, proposed in cond-mat/0003453, corresponding to the non-standard filling nu =1/(p+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering our partition function naturally go to complete a Z_2-orbifold construction of the CFT for the Halperin state. Different behaviours for the p even and p odd cases are also studied. Finally it is shown that the tunneling phenomenon selects out a twist invariant CFT which is identified with the Moore-Read model.