Influence of boundary conditions on level statistics and eigenstates at the metal insulator transition

TL;DR

This paper examines how boundary conditions affect the statistical properties of energy levels and eigenstates at the metal-insulator transition in various disordered quantum models, revealing boundary-dependent spectral statistics but boundary-independent eigenstate correlations.

Contribution

It provides a detailed numerical analysis of boundary condition effects on level statistics and eigenstate correlations at the critical point of metal-insulator transitions in different symmetry classes.

Findings

Level spacing distributions differ for periodic and Dirichlet boundary conditions.

Critical disorder strength remains unchanged despite boundary condition variations.

Eigenstate correlations associated with anomalous diffusion are unaffected by boundary changes.

Abstract

We investigate the influence of the boundary conditions on the scale invariant critical level statistics at the metal insulator transition of disordered three-dimensional orthogonal and two-dimensional unitary and symplectic tight-binding models. The distribution of the spacings between consecutive eigenvalues is calculated numerically and shown to be different for periodic and Dirichlet boundary conditions whereas the critical disorder remains unchanged. The peculiar correlations of the corresponding critical eigenstates leading to anomalous diffusion seem not to be affected by the change of the boundary conditions.