Exponential decay properties of Wannier functions and related quantities

Abstract

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of non-orthonormal Wannier-like functions.

4 pages, with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/lh_wann/index.html

Cited by in corpus (93)

• Many-Body Physics with Ultracold Gases
• Maximally localized Wannier functions: Theory and applications
• Wannier90 as a community code: new features and applications
• Electron-phonon interactions from first principles
• Topolectrical circuits
• Nearsightedness of Electronic Matter
• O(N) methods in electronic structure calculations
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Spectral and Fermi surface properties from Wannier interpolation
• Topological Non-Hermitian skin effect
• The Insulating State of Matter: A Geometrical Theory
• Van der Waals interactions in DFT made easy by Wannier functions
• Band Structure and Quantum Conductance of Nanostructures from Maximally-Localized Wannier Functions: The Case of Functionalized Carbon Nanotubes
• Accurate and efficient linear scaling DFT calculations with universal applicability
• The insulator/Chern-insulator transition in the Haldane model
• Daubechies Wavelets for Linear Scaling Density Functional Theory
• Electron localization in the insulating state: application to crystalline semiconductors
• Charge Transfer as a Ubiquitous Mechanism in Determining the Negative Charge at Hydrophobic Interfaces
• Challenges in Large Scale Quantum Mechanical Calculations
• First-principles predictions of Hall and drift mobilities in semiconductors
• Theory of Orbital Magnetization in Solids
• Large scale and linear scaling DFT with the CONQUEST code
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• TeaNet: universal neural network interatomic potential inspired by iterative electronic relaxations
• Band structure engineering of ideal fractional Chern insulators
• Ultracold bosons with short-range interaction in regular optical lattices
• Accurate ionic forces and geometry optimisation in linear scaling density-functional theory with local orbitals
• Imaging nodal knots in momentum space through topolectrical circuits
• Exceptional Bound States and negative Entanglement Entropy
• Automated high-throughput Wannierisation
• Linear-scaling time-dependent density-functional theory in the linear response formalism
• Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
• Accurate polarization within a unified Wannier function formalism
• Ab initio derivation of Hubbard models for cold atoms in optical lattices
• Dimensional transmutation from non-Hermiticity
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Calculating optical absorption spectra for large systems using linear-scaling density-functional theory
• Van der Waals interactions at surfaces by DFT using Wannier functions
• Designing non-Hermitian real spectra through electrostatics
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• Norm estimates of complex symmetric operators applied to quantum systems
• Band flatness optimization through complex analysis
• Using ONETEP for accurate and efficient O(N) density functional calculations
• Ab initio complex band structure of conjugated polymers: Effects of hydrid DFT and GW schemes
• Exact holographic mapping in free fermion systems
• Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: an application to graphene
• Tight binding models for ultracold atoms in honeycomb optical lattices
• Gradient-based stochastic estimation of the density matrix
• Bloch dynamics in lattices with long range hoppings
• A Unified Perspective of Complex Band Structure: Interpretations, Formulations, and Applications
• Analytic structure of Bloch functions for linear molecular chains
• Spatial decay of the single-particle density matrix in insulators: analytic results in two and three dimensions
• Dipole-dipole interactions in optical lattices do not follow an inverse cube power law
• Topological Phase Transition and Charge Pumping in a One-Dimensional Periodically Driven Optical Lattice
• Origin of band flatness and constraints of higher Chern numbers
• Geometric phases and Wannier functions of Bloch electrons in 1-dimension
• Modal expansions in periodic photonic systems with material loss and dispersion
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Spatial decay of the single-particle density matrix in tight-binding metals: +AFwAXA- analytic results in two dimensions
• Fragment Approach to Constrained Density Functional Theory Calculations using Daubechies Wavelets
• Efficient Evaluation of Exact Exchange for Periodic Systems via Concentric Atomic Density Fitting
• Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wavefunction Perturbation
• van der Waals-corrected Density Functional Theory simulation of adsorption processes on noble-metal surfaces: Xe on Ag(111), Au(111), and Cu(111)
• A Local Representation of the Electronic Dielectric Response Function
• Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices
• A simple model for multiple-choice collective decision making
• "Quantum bipolaron" superconductivity from quadratic electron-phonon coupling
• Maximally localized Wannier functions within the (L)APW+LO method
• Ab initio calculation of Hubbard parameters for Rydberg-dressed atoms in an one-dimensional optical lattice
• Higher dimensional Wannier functions of multi-parameter Hamiltonians
• Universality of Boundary Charge Fluctuations
• Exact results for spatial decay of the one-body density matrix in low-dimensional insulators
• Tracing potential energy surfaces of electronic excitations via their transition origins: application to Oxirane
• One-dimensional s-p superlattice
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Overlaying optical lattices for simulation of complex frustrated antiferromagnets
• Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation
• Real-Time Corrections to the Effective Potential
• Exact results for spatial decay of correlations in low-dimensional insulators II
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Exploring phonon-like interactions in one-dimensional Bose-Fermi mixtures
• Wannier functions of elliptic one-gap potentials
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• Building bridges: matching density functional theory with experiment
• Topological edge states in bowtie ladders with different cutting edges
• Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic Orbitals
• O(N) algorithms for disordered systems
• Exact Mappings in Condensed Matter Physics
• Calculation of Berry curvature using nonorthogonal atomic orbitals
• Spatial decay of the one-body density matrix in insulators revised