Halperin (m, m',n) bilayer quantum Hall states on thin cylinders

Abstract

The Halperin $(m,m^{\prime },n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the $(331)$ state and the non-abelian Moore-Read state in the thin cylinder limit.

published version

References in corpus (4)

• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• One-Dimensional Theory of the Quantum Hall System
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Cited by in corpus (2)

• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Pfaffian statistics through adiabatic transport in the 1D coherent state representation