Boundary effective action for quantum Hall states

TL;DR

This paper analyzes the boundary effective actions in quantum Hall states, identifying four Chern-Simons terms that determine edge physics, including protected gapless modes and boundary responses like Hall viscosity.

Contribution

It clarifies the role of four Chern-Simons terms in quantum Hall boundary physics, especially highlighting the non-protection of some responses by gapless modes.

Findings

Two terms protect gapless edge modes related to Hall conductance.

Wen-Zee term contributes to Hall viscosity and boundary response.

Coefficient of Wen-Zee term can vary without gap closure or symmetry breaking.

Abstract

We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective action of the state. Two of these protect gapless edge modes. They describe Hall conductance and, with some provisions, thermal Hall conductance. The remaining two, including the Wen-Zee term, which contributes to the Hall viscosity, do not protect gapless edge modes but are instead related to local boundary response fixed by symmetries. We highlight some basic features of this response. It follows that the coefficient of the Wen-Zee term can change across an interface without closing a gap or breaking a symmetry.