Critical level statistics of a quantum Hall system with Dirichlet boundary conditions

TL;DR

This study numerically examines how Dirichlet boundary conditions affect the level spacing distribution in a quantum Hall system, revealing boundary-dependent shifts in critical energies and distributions.

Contribution

It demonstrates that boundary conditions significantly influence the critical level statistics and energy positions in quantum Hall systems, highlighting the importance of boundary effects.

Findings

Edge states cause the critical energy to shift with system size under Dirichlet conditions.

Different boundary conditions lead to distinct scale-invariant level spacing distributions.

Extrapolation shows boundary-dependent critical distributions in the thermodynamic limit.

Abstract

We investigate numerically the influence of Dirichlet boundary conditions on the nearest neighbor level spacing distribution $P(s)$ of a two-dimensional disordered tight-binding model in the presence of a strong perpendicular magnetic field. From the calculation of the second moment of $P(s)$ it is shown that for Dirichlet boundary conditions, due to the presence of edge states, the position of the critical energy shifts with increasing system size to the location of the critical energy for periodic boundary conditions. An extrapolation to infinite system size results in different critical (scale independent) $P(s)$ distributions for periodic and Dirichlet boundary conditions.