Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder

Abstract

We resolve the problem of the violation of single parameter scaling at the zero energy of the Anderson tight-binding model with diagonal disorder. It follows from the symmetry properties of the tight-binding Hamiltonian that this spectral point is in fact a boundary between two adjacent bands. The states in the vicinity of this energy behave similarly to states at other band boundaries, which are known to violate single parameter scaling.

arXiv commentrevised version, 4 pages, 2 figures, revtex

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• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Strong-disorder renormalization-group study of the one-dimensional tight-binding model
• T-duality in supersymmetric theory of disordered quantum systems
• Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics
• Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach
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• Probing Band-center Anomaly with the Kernel Polynomial Method
• Anomalous localisation in the aperiodic Kronig-Penney model
• Interaction-induced connectivity of disordered two-particle states
• Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model
• Fluctuations of the product of random matrices and generalized Lyapunov exponent
• Resonant enhancement of Anderson localization: Analytical approach
• Crossover of conductance and local density of states in a single-channel disordered quantum wire
• Statistics of transmission in one-dimensional disordered systems: universal characteristics of states in the fluctuation tails
• Decoherence-induced conductivity in the discrete 1D Anderson model: A novel approach to even-order generalized Lyapunov exponents
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• Localization length versus level repulsion in 1-D driven disordered quantum wires
• Metal - Insulator Transition in 3D Quantum Percolation
• The band-centre anomaly in the 1D Anderson model with correlated disorder
• Critical States Embedded in the Continuum
• Scaling properties of one-dimensional off-diagonal disorder
• Conductance of a quantum dot in the Kondo regime connected to dirty wires
• Unified description of perturbation theory and band center anomaly in one-dimensional Anderson localization
• Transmission of waves through a pinned elastic medium
• Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model
• Anomalies in conductance and localization length of disordered ladders