Non-universal corrections to the level curvature distribution beyond random matrix theory

TL;DR

This paper investigates deviations from random matrix theory in the level curvature distribution for T-breaking perturbations, highlighting the role of gauge invariance and dimensionality in the corrections.

Contribution

It calculates the leading correction to the level curvature distribution beyond RMT using the nonlinear sigma-model, considering gauge invariance effects and dimensionality.

Findings

Correction sign depends on gauge invariance presence.

Different effects for vector-potential and magnetic field perturbations.

Dimensionality influences level statistics in dirty metals.

Abstract

The level curvature distribution function is studied beyond the random matrix theory for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the level curvature distribution is calculated using the nonlinear sigma-model. The sign of the correction depends on the presence or absence of the global gauge invariance and is different for perturbations caused by the constant vector-potential and by the random magnetic field. Scaling arguments are discussed that indicate on the qualitative difference in the level statistics in the dirty metal phase for space dimensionalities $d<4$ and $d>4$.