Universal edge transport in interacting Hall systems

TL;DR

This paper proves quantized edge conductance in interacting 2D Hall systems, reveals universal relations for edge properties, and demonstrates spin-charge separation using advanced mathematical methods.

Contribution

It establishes the quantization of edge conductance and universal scaling relations in interacting Hall systems, extending known results to many-body lattice models.

Findings

Quantized edge charge conductance in interacting models

Universal scaling relations for edge Drude weight and susceptibility

Observation of spin-charge separation in edge excitations

Abstract

We study the edge transport properties of $2d$ interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin-charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof.