Anomalous Bulk Current in Quantum Hall Systems with an Expanding Edge

TL;DR

This paper explores the energy flux and anomalous currents in quantum Hall systems with expanding edges, linking gravitational anomalies to observable effects in bulk and edge regions.

Contribution

It extends previous models to include bulk and edge regions, demonstrating how gravitational anomalies induce non-trivial currents due to edge expansion.

Findings

Covariant gravitational anomaly appears on the edge via anomaly-inflow.

Energy flux on the edge is analyzed through gravitational and Weyl anomalies.

Anomalous edge currents induce non-trivial bulk currents due to edge expansion.

Abstract

Understanding topological phases of matter is essential for advancing both the fundamental theory and practical applications of condensed matter physics. Recently, a theoretical framework for a quantum Hall system with an expanding edge state was proposed [Phys. Rev. D {\bf 105}, 105009 (2022)], revealing the existence of an energy flux analogous to Hawking radiation on the edge. Motivated by this work, we extend the analysis to a model of a $(2+1)$-dimensional spacetime that includes both the bulk and edge regions. Due to the presence of bulk and edges, we demonstrate that the covariant form of the gravitational anomaly appears on the edge via the anomaly-inflow mechanism. Then, we investigate the energy flux on the edge from the viewpoint of gravitational anomalies, such as covariant gravitational and Weyl anomalies. We also find that, due to the conservation of energy and momentum in the entire system, the presence of anomalous currents on the expanding edge induces non-trivial currents in the bulk originating from the expansion of the edge.