${\mathcal{L}}^2$ localization landscape for highly-excited states

Abstract

The localization landscape gives direct access to the localization of bottom-of-band eigenstates in non-interacting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal degrees of freedom by introducing a modified ${\mathcal{L}}^2$-landscape, and we demonstrate its accuracy in a variety of archetypal models of Anderson localization in one and two dimensions. This ${\mathcal{L}}^2$-landscape function can be efficiently computed using hierarchical methods that allow evaluating the diagonal of a well-chosen Green function. We compare our approach to other landscape methods, bringing new insights on their strengths and limitations. Our approach is general and can in principle be applied to both studies of topological Anderson transitions and many-body localization.

arXiv comment6.5 + 1 pages, all comments are welcome

References in corpus (40)

• Topological Insulators
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• 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
• Scaling Theory of the Integer Quantum Hall Effect
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Many-body localization: an introduction and selected topics
• Two Dimensional Quantum Mechanical Modeling of Nanotransistors
• Recent progress in many-body localization
• Demonstration of one-parameter scaling at the Dirac point in graphene
• The spin quantum Hall effect in unconventional superconductors
• Fluctuations of the inverse participation ratio at the Anderson transition
• Topological delocalization of two-dimensional massless Dirac fermions
• The recursive Green's function method for graphene
• Exact exponents for the spin quantum Hall transition
• Quasiparticle localization in superconductors with spin-orbit scattering
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Localization landscape theory of disorder in semiconductors. III. Application to carrier transport and recombination in light emitting diodes
• Quasiparticle transport and localization in high-T_c superconductors
• Two-dimensional conformal field theory for disordered systems at criticality
• Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond
• Gaussian field theories, random Cantor sets and multifractality
• Effective confining potential of quantum states in disordered media
• Localization landscape theory of disorder in semiconductors II: Urbach tails of disordered quantum well layers
• Delocalization in coupled one-dimensional chains
• Localization landscape theory of disorder in semiconductors I: Theory and modeling
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Fokker-Planck equations and density of states in disordered quantum wires
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Spectral and Transport Properties of d-Wave Superconductors With Strong Impurities
• Absence of a metallic phase in charge-neutral graphene with a random gap
• Conductivity of disordered graphene at half filling
• Anderson localization and the topology of classifying spaces
• Many-Body Localization Landscape
• Extension and optimization of the FIND algorithm: computing Green's and less-than Green's functions (with technical appendix)
• Localization landscape for Dirac fermions

Cited by in corpus (6)

• Quantum states in disordered media. I. Low-pass filter approach
• Crossover Between Quantum and Classical Waves and High Frequency Localization Landscapes
• Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls
• A stochastic method to compute the $L^2$ localisation landscape
• Higher-order localization landscape theory of Anderson localization
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations