Boundary multifractality in critical one-dimensional systems with long-range hopping

2006/11/30 by A. Mildenberger, Arvind R. Subramaniam, A. R. Subramaniam +7
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.75.094204

published as Phys. Rev. B 75, 094204 (2007) · 7 pages, 4 figures, some typos corrected

openalex publication_date 2007/03/29 · arxiv created 2007/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Weak chaos in a quantum Kepler problem
• f(α)multifractal spectrum at strong and weak disorder
• Termination of Multifractal behavior for Critical Disordered Dirac Fermions
• Exact Relations between Multifractal Exponents at the Anderson Transition
• Two-level correlation function of critical random-matrix ensembles
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• Magnetic properties of Sr₂Fe₁+xMo₁-xO₆ with -1 <= x <= 0.25