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

TL;DR

This paper investigates Halperin bilayer quantum Hall states on thin cylinders, revealing charge density wave patterns, torus degeneracies, and phase transitions, with connections to spin chain physics and non-abelian states.

Contribution

It provides a detailed analysis of Halperin (m,m',n) states on thin cylinders, including charge patterns, degeneracies, and phase transition behavior, extending understanding of these states in reduced geometries.

Findings

Charge density wave patterns characteristic of quantum Hall states are identified.

Torus degeneracies are recovered in the thin cylinder limit.

Phase transition between (331) and Moore-Read states is analyzed.

Abstract

The Halperin $(m,m',n)$ 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.