Universal edge transport in interacting Hall systems

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.

63 pages, 2 figures. Proof adapted to a larger class of hopping Hamiltonians. Minor corrections, typos fixed. Accepted for publication on Comm. Math. Phys

References in corpus (10)

• Correlation effects in two-dimensional topological insulators
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Equality of the bulk and edge Hall conductances in a mobility gap
• Bulk-Edge correspondence for two-dimensional Floquet topological insulators
• Topological edge states and quantum Hall effect in the Haldane model
• Non perturbative Adler-Bardeen Theorem
• Topological phase transitions and universality in the Haldane-Hubbard model
• Haldane relation for interacting dimers
• Spin Hall insulators beyond the Helical Luttinger model
• Canonical Drude weight for non-integrable quantum spin chains

Cited by in corpus (8)

• Correlation Energy of a Weakly Interacting Fermi Gas
• A new approach to transport coefficients in the quantum spin Hall effect
• Quantization of the interacting Hall conductivity in the critical regime
• Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems
• Drude weight increase by orbital and repulsive interactions in fermionic ladders
• From orbital magnetism to bulk-edge correspondence
• Adiabatic Evolution of Low-Temperature Many-Body Systems
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure