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

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.

7 pages, 4 figures, some typos corrected

References in corpus (4)

• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Multifractality of Hamiltonians with power-law transfer terms
• Long range disorder and Anderson transition in systems with chiral symmetry
• Two-level correlation function of critical random-matrix ensembles

Cited by in corpus (7)

• Anderson Transitions
• Fractional Laplacian in Bounded Domains
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• Boundary criticality and multifractality at the 2D spin quantum Hall transition
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Statistics of the two-point transmission at Anderson localization transitions
• Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry