Quantization of the Interacting Hall Conductivity in the Critical Regime

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological Phases

Background:

• The Haldane model is a foundational 2D lattice model for the integer quantum Hall effect.
• Previous studies were limited to perturbative regimes, far from critical transition lines.

Purpose of the Study:

• To analyze the Hall conductivity in an interacting version of the Haldane model.
• To investigate the impact of short-range electron-electron interactions on topological phase transitions.

Main Methods:

• Mathematical proof for quantized Hall conductivity under specific interaction conditions.
• Construction of critical curves modified by electron-electron interactions.
• Application of renormalization group methods to resolve divergences.

Main Results:

• Hall conductivity remains quantized for parameters outside two critical curves.
• Topological phase transitions occur at these critical curves, causing abrupt changes in the Hall coefficient.
• Electron-electron interactions 'dress' the critical curves, shifting them from predictions based on non-interacting models.

Conclusions:

• The non-renormalization of Hall conductivity is linked to lattice conservation laws and current-current correlation properties.
• The study provides a complete construction of interaction-modified critical curves.
• Renormalization group methods are essential for accurately describing the interacting system and its phase transitions.