Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
arXiv:cond-mat/0412669 · doi:10.1103/PhysRevB.71.174203
Abstract
We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al., J. Phys. A: Math. Gen. 33, L161 (2000)] that this model reveals a localization-delocalization transition with respect to the disorder magnitude provided . The transition occurs at one of the band edges (the upper one for and the lower one for). The states at the other band edge are always localized, which hints on the existence of a single mobility edge. We analyze the mobility edge and show that, although the number of delocalized states tends to infinity, they form a set of null measure in the thermodynamic limit, i.e. the mobility edge tends to the band edge. The critical magnitude of disorder for the band edge states is computed versus the interaction exponent by making use of the conjecture on the universality of the normalized participation number distribution at transition.
7 pages, 6 postscript figures, uses revtex4
References in corpus (25)
- Random-Matrix Theory of Quantum Transport
- Statistics of energy levels and eigenfunctions in disordered systems
- Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Statistics and Scaling in Disordered Mesoscopic Electron Systems
- Fluctuations of the inverse participation ratio at the Anderson transition
- Multifractality and critical fluctuations at the Anderson transition
- Experimental evidence of delocalized states in random dimer superlattices
- Experimental observation of the mobility edge in a waveguide with correlated disorder
- Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
- Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach
- Delocalization in harmonic chains with long-range correlated random masses
- Critical Hamiltonians with long range hopping
- Microscopic Theory of Dipole-Exchange Spin Waves in Ferromagnetic Films: Linear and Nonlinear Processes
- Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange
- Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems
- Absence of localization and large dc conductance in random superlattices with correlated disorder
- Localization of Electronic States in Chain Model Based on Real DNA Sequence
- Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction
- Enhanced suppresion of localization in a continuous Random-Dimer Model
- New class of level statistics in correlated disordered chains
- Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder
- Phase coherence in tight-binding models with nonrandom long-range hopping
- Three-dimensional effects on extended states in disordered models of polymers
- Selective Transport and Mobility Edges in Quasi-1D Systems with a Stratified Correlated Disorder
Cited by in corpus (43)
- Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Correlation-induced localization
- Shielding and localization in presence of long range hopping
- Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities
- Robustness of delocalization to the inclusion of soft constraints in long-range random models
- Mobility edge and multifractality in a periodically driven Aubry-André model
- Criticality of Spin Systems with Weak Long-Range Interactions
- Anomalous transport through algebraically localized states in one-dimension
- Non-ergodic delocalized phase with Poisson level statistics
- Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
- Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
- Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices
- Disorder-enhanced transport in a chain of lossy dipoles strongly coupled to cavity photons
- Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
- Localization of soft modes at the depinning transition
- Anisotropy-mediated reentrant localization
- Signatures of multifractality in a periodically driven interacting Aubry-André model
- Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
- Dynamical localization of interacting bosons in the few-body limit
- Transition between localized and extended states in the hierarchical Anderson model
- Grover-like search via Frenkel exciton trapping mechanism
- Quantum walk and Anderson localization of rotational excitations in disordered ensembles of polar molecules
- Multifractal analysis of eigenvectors of smallworld networks
- Effects of long range hopping in the Bose-Hubbard model
- Emergent multifractality in power-law decaying eigenstates
- The renormalization flow of the hierarchical Anderson model at weak disorder
- Non-Anderson critical scaling of the Thouless conductance in 1D
- Duality between disordered nodal semimetals and systems with power-law hopping
- Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation
- Single-particle localization in a two-dimensional Rydberg spin system
- More current with less particles due to power-law hopping
- Accurate densities of states for disordered systems from free probability: Live Free or Diagonalize
- Diffusion of excitation and power-law localization in long-range-coupled strongly disordered systems
- Tail states and unusual localization transition in low-dimensional Anderson model with power-law hopping
- Bound states in one-dimensional systems with colored noise
- Excitation transfer in disordered spin chains with long-range exchange interactions
- Localization and delocalization in one-dimensional systems with translation-invariant hopping
- Spread of Correlations in Strongly Disordered Lattice Systems with Long-Range Coupling
- Quantum walks assisted by particle number fluctuations
- Design Principles for Enhanced Quantum Transport with Site-Dependent Noise
- Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking
- Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder