Mapping the Current-Current Correlation Function Near a Quantum Critical Point

TL;DR

This paper derives an asymptotic formula for the current-current correlation function near a quantum critical point and validates it through numerical simulations in the disordered Hofstadter model, enhancing understanding of electron transport at criticality.

Contribution

It introduces a new asymptotic formula for the current-current correlation function near quantum critical points and confirms it with numerical simulations in a specific model.

Findings

Derived an asymptotic formula for the correlation function near criticality

Numerical simulations in the Hofstadter model confirm theoretical predictions

Enhanced understanding of transport properties near quantum phase transitions

Abstract

The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau-insulator or plateau-plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current-current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current-current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.