Emergent particle-hole symmetry in the half-filled Landau level

TL;DR

This paper develops an effective theory for a particle-hole symmetric state in a half-filled Landau level, using a strip construction that reveals emergent Dirac fermion behavior and symmetry properties.

Contribution

It introduces a strip-based model that demonstrates particle-hole symmetry emergence and connects to Dirac fermion descriptions in quantum Hall systems.

Findings

System exhibits particle-hole symmetry at long distances.

System described by Dirac fermions coupled to gauge fields.

Supports the Son Dirac composite fermion theory.

Abstract

We provide an effective description of a particle-hole symmetric state of electrons in a half-filled Landau level, starting from the traditional approach pioneered by Halperin, Lee and Read. Specifically, we study a system consisting of alternating quasi-one-dimensional strips of composite Fermi liquid (CFL) and composite hole liquid (CHL), both of which break particle-hole symmetry. When the CFL and CHL strips are identical in size, the resulting state is manifestly invariant under the combined action of a particle-hole transformation with respect to a single Landau level (which interchanges the CFL and CHL) and translation by one unit, equal to the strip width, in the direction transverse to the strips. At distances long compared to the strip width, we demonstrate that the system is described by a Dirac fermion coupled to an emergent gauge field, with an anti-unitary particle-hole symmetry, as recently proposed by Son.