Anderson localization: a density matrix approach

Abstract

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the standard transfer matrix method, we extract the localization length from the modular density matrix in quasi-one-dimensional systems. This approach successfully captures the metal-insulator transition in the three-dimensional Anderson model and in the two-dimensional Anderson model with spin-orbit coupling. It can be also readily extended to multiorbital systems. We further generalize the formalism to interacting systems, showing that the one-dimensional spinless attractive model exhibits the expected metallic phase, consistent with previous studies. More importantly, we demonstrate the existence of a two-dimensional metallic phase in the presence of Hubbard interactions and disorder. This method offers a new perspective on Anderson localization and its interplay with interactions.

10 pages, 7 figures in the main text, and 13 pages, 9 figures in the Appendix

References in corpus (45)

• The density-matrix renormalization group
• Maximally localized Wannier functions: Theory and applications
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• Unbounded growth of entanglement in models of many-body localization
• The ITensor Software Library for Tensor Network Calculations
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Area laws in a many-body localized state and its implications for topological order
• Metal-insulator transition in two-dimensional electron systems
• Entanglement entropy of random quantum critical points in one dimension
• The Insulating State of Matter: A Geometrical Theory
• A practical guide to density matrix embedding theory in quantum chemistry
• Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems
• Many-body localization characterized from a one-particle perspective
• Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons
• Multifractal finite-size-scaling and universality at the Anderson transition
• Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
• Flow diagram of the metal-insulator transition in two dimensions
• Inhomogeneous metallic phase upon disordering a two dimensional Mott insulator
• Anderson localization vs. Mott-Hubbard metal-insulator transition in disordered, interacting lattice fermion systems
• Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator
• Entanglement entropy in one-dimensional disordered interacting system: The role of localization
• One-particle-density-matrix occupation spectrum of many-body localized states after a global quench
• On Large Scale Diagonalization Techniques for the Anderson Model of Localization
• Study of off-diagonal disorder using the typical medium dynamical cluster approximation
• Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice
• Entanglement properties and quantum phases for a fermionic disordered one dimensional wire with attractive interactions
• Scaling and renormalization in the modern theory of polarization: application to disordered systems
• Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems
• Study of multiband disordered systems using the typical medium dynamical cluster approximation
• Disorder and Interactions in 1D Systems
• Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N
• Metal-Insulator-Transition in a Weakly interacting Disordered Electron System
• Friedel oscillations in disordered quantum wires: Influence of e-e interactions on the localization length
• Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions
• Do metals exist in two dimensions? A study of many-body localisation in low density electron gas
• Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective
• On the Nature of Localization in Ti doped Si
• Interacting lattice electrons with disorder in two dimensions: Numerical evidence for a metal-insulator transition with a universal critical conductivity
• Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition