Effect of a magnetic flux on the critical behavior of a system with long range hopping

TL;DR

This paper investigates how magnetic flux influences the critical behavior and spectral correlations of a one-dimensional disordered system with long-range hopping, revealing a transition from orthogonal to unitary symmetry and connections to the Calogero-Sutherland model.

Contribution

It demonstrates that the system remains at the metal-insulator transition for all disorder levels and links spectral correlations to the Calogero-Sutherland model at finite temperature.

Findings

Spectral correlations follow critical statistics.

Smooth symmetry transition with flux in weak disorder.

Flux independence of correlations in strong disorder.

Abstract

We study the effect of a magnetic flux in a 1D disordered wire with long range hopping. It is shown that this model is at the metal-insulator transition (MIT) for all disorder values and the spectral correlations are given by critical statistics. In the weak disorder regime a smooth transition between orthogonal and unitary symmetry is observed as the flux strength increases. By contrast, in the strong disorder regime the spectral correlations are almost flux independent. It is also conjectured that the two level correlation function for arbitrary flux is given by the dynamical density-density correlations of the Calogero-Sutherland (CS) model at finite temperature. Finally we describe the classical dynamics of the model and its relevance to quantum chaos.