Modular symmetry and temperature flow of conductivities in quantum Hall systems with varying Zeeman energy

TL;DR

This paper investigates how the critical point between quantum Hall plateaux shifts with Zeeman energy changes, using modular symmetry to analyze temperature-dependent conductivity flows in particle-hole symmetric samples.

Contribution

It introduces a modular symmetry framework to analyze the temperature flow of conductivities as Zeeman energy varies in quantum Hall systems.

Findings

Flow diagrams show distinct temperature-dependent conductivity behaviors at different Zeeman energies.

Modular symmetry constrains the possible flow trajectories of conductivities.

Results support the law of corresponding states in quantum Hall systems with varying Zeeman energy.

Abstract

The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the conductivities as a function of temperature, with the magnetic field fixed, are constructed for different Zeeman energies, for samples with particle-hole symmetry.