Boundary multifractality in critical 1D systems with long-range hopping

TL;DR

This paper investigates boundary multifractality in a critical 1D system with long-range hopping, revealing that boundary critical behavior depends on an additional parameter beyond bulk properties.

Contribution

It introduces the boundary critical theory for the PRBM model, showing boundary behavior is influenced by boundary-specific parameters, not just bulk criticality.

Findings

Boundary multifractality analyzed both analytically and numerically.

Boundary criticality depends on an extra parameter related to boundary hopping.

Bulk properties do not fully determine boundary critical behavior.

Abstract

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary.