Critical Hamiltonians with long range hopping
arXiv:cond-mat/9908178 · doi:10.1002/(SICI)1521-3889(199911)8:7/9<697::AID-ANDP697>3.0.CO;2-W
Abstract
Critical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG flow of the distribution of coupling parameters is characterized by a family of non-trivial fix points. We consider the RG flow of the distribution of participation ratios of eigenstates. Scaling of participation ratios is sensitive to the nature of the RG fix point. For some fix points, scaling of participation ratios is characterized by a distribution of exponents, rather than by a single exponent. The RG method can be generalized to treat certain fermionic Hamiltonians with disorder and long range hopping. We derive the RG for a model of interacting two-level systems. Besides couplings, in this problem the RG includes the density of states. The density of states is renormalized so that it develops a singularity near zero energy.
10 pages, 5 eps figures, LaTeX uses annalen.cls style (included), proceedings of Localization 99
References in corpus (1)
Cited by in corpus (52)
- Anderson Transitions
- Fluctuations of the inverse participation ratio at the Anderson transition
- Many-body Localization with Dipoles
- Multifractality and critical fluctuations at the Anderson transition
- Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
- Anderson localisation in tight-binding models with flat bands
- Many-body localization transition with power-law interactions: Statistics of eigenstates
- Fluctuations of the correlation dimension at metal-insulator transitions
- Marginal Anderson localization and many body delocalization
- Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
- Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
- Clustering of non-ergodic eigenstates in quantum spin glasses
- Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction
- Multifractal spectrum at strong and weak disorder
- Virial expansion for almost diagonal random matrices
- Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
- Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
- High values of disorder-generated multifractals and logarithmically correlated processes
- Supersymmetry Approach to Almost Diagonal Random Matrices
- Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
- Multifractality of Hamiltonians with power-law transfer terms
- Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
- Possible many-body localization in a long-lived finite-temperature ultracold quasi-neutral molecular plasma
- Level compressibility in a critical random matrix ensemble: The second virial coefficient
- Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms
- Dynamics of Disordered Quantum Systems Using Flow Equations
- Density of states for almost diagonal random matrices
- Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
- Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
- Statistics of the two-point transmission at Anderson localization transitions
- Genuine localisation transition in a long-range hopping model
- Supersymmetric Virial Expansion for Time-Reversal Invariant Disordered Systems
- A critical Dyson hierarchical model for the Anderson localization transition
- Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
- What are the interactions in quantum glasses?
- Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
- Many-body physics with ultracold plasmas: Quenched randomness and localization
- Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
- Energy delocalization in strongly disordered systems induced by the long-range many-body interaction
- Two-level correlation function of critical random-matrix ensembles
- Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder
- Critical level spacing distribution in long-range hopping Hamiltonians
- Critical properties in long-range hopping Hamiltonians
- Towards rigorous analysis of the Levitov-Mirlin-Evers recursion
- Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry
- Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
- Anderson transition of the plasma oscillations of 1D disordered Wigner lattices
- Energy-level statistics in strongly disordered systems with power-law hopping
- Negative effective mass transition and anomalous transport in power-law hopping bands
- Disordered statistical physics in low dimensions: extremes, glass transition, and localization
- Statistical properties of two-particle transmission at Anderson transition
- Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: a relay-race mechanism