Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems

Abstract

We test the usefulness of a generalized inverse participation ratio (GIPR) as a measure of Anderson localization. The GIPR differs from the usual inverse participation ratio in that it depends on the local density of states rather than on the single-electron wavefunctions. This makes it suitable for application to many-body systems. We benchmark the GIPR by performing a finite-size scaling analysis of a disordered, noninteracting, three-dimensional tight-binding lattice. We find values for the critical disorder and critical exponents that are in agreement with published values.

6 pages, 5 figures Accepted for publication in PRB

References in corpus (29)

• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Metallic behavior and related phenomena in two dimensions
• Statistics of energy levels and eigenfunctions in disordered systems
• Corrections to scaling at the Anderson transition
• Delocalization of a disordered bosonic system by repulsive interactions
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems
• Multifractality and critical fluctuations at the Anderson transition
• Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons
• Anderson localization in Bose-Einstein condensates
• Strongly interacting bosons in a disordered optical lattice
• Disorder-Driven Non-Fermi Liquid Behavior of Correlated Electrons
• Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
• Inhomogeneous metallic phase upon disordering a two dimensional Mott insulator
• Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions
• Disorder Screening in Strongly Correlated Systems
• Dimensionality dependence of the wave function statistics at the Anderson transition
• Dynamical Mean Field Study of the Two-Dimensional Disordered Hubbard Model
• Single-particle excitations under coexisting electron correlation and disorder: a numerical study of the Anderson-Hubbard model
• Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder
• Universality of the metal-insulator transition in three-dimensional disordered systems
• The geometrically-averaged density of states as a measure of localization
• Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions
• Determinant Quantum Monte Carlo Study of the Screening of the One Body Potential near a Metal-Insulator Transition
• Static Screening and Delocalization Effects in the Hubbard-Anderson Model
• The geometrically-averaged density of states calculated from the local Green's function as a measure of localization

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