Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

Abstract

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_c=16.5$ and the critical exponent $\nu =1.34$ are computed.

9 pages, Latex, 6 PostScript figures in uuencoded compressed tar file are appended

References in corpus (1)

• Critical Exponents for the Metal--Insulator Transition in Disordered Systems

Cited by in corpus (40)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization
• Boundary conditions at the mobility edge
• Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
• Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?
• Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles
• Universality and the QCD Anderson Transition
• Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model
• Spectral Correlations from the Metal to the Mobility Edge
• Energy-level statistics at the metal-insulator transition in anisotropic systems
• Critical spectral statistics in two-dimensional interacting disordered systems
• Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models
• Universal Fluctuations in Spectra of Disordered Systems at the Anderson Transition
• Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition
• Replacing energy by von Neumann entropy in quantum phase transitions
• Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles
• Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions
• Renormalization group approach to energy level statistics at the integer quantum Hall transition
• Deconfinement, chiral transition and localisation in a QCD-like model
• Critical Level Statistics in Two-dimensional Disordered Electron Systems
• One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
• Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling
• Few-boson localization in a continuum with speckle disorder
• An Anderson-like model of the QCD chiral transition
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Universal level-spacing statistics in quasiperiodic tight-binding models
• Application of random matrix theory to quasiperiodic systems
• Critical behaviour at the metal-insulator transition in 3-dimensional disordered systems in a strong magnetic field
• Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians
• Real-space renormalization-group approach to the integer quantum Hall effect
• On the localization transition in three dimensions: Monte-Carlo simulation of a non-linear $\sigma$-model
• Metal-insulator transition in disordered systems from the one-body density matrix
• Scaling Behavior of Level Statistics in Quantum Hall Regime
• Spectral Properties of Three Dimensional Layered Quantum Hall Systems
• Mobility Edge and Level Statistics of Random Tight-Binding Hamiltonians
• Localization of non-interacting electrons in thin layered disordered systems
• Smoothed universal correlations in the two-dimensional Anderson model
• Critical Exponent of the Localization Length for the Symplectic Case
• Disorder and Interactions in Graphene and other Quantum Systems