Determining topological order from a local ground state correlation function

Abstract

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological insulators and the Z index of the integer quantum Hall effect manifest themselves locally. We do so by providing an algorithm for determining these indices from a local equal time ground-state correlation function at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder and can be naturally generalized to include weak interactions. The locality of these topological indices implies bulk-edge correspondence theorem.

7 pages, 3 figures. Major changes: the paper was divided into sections, the locality of the order in 3D topological insulators is also discussed

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• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Quantum anomalous Hall effect and related topological electronic states
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Mapping topological order in coordinate space
• Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure
• The strong side of weak topological insulators
• Seeing topological order in time-of-flight measurements
• Scattering theory of topological insulators and superconductors
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Exploration and prediction of topological electronic materials based on first-principles calculations
• Topological insulators from the Perspective of first-principles calculations
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Probing bulk topological invariants using leaky photonic lattices
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Phonon-induced renormalization of electron wave functions
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories
• Topology in quasicrystals
• Strictly local tensor networks for short-range topological insulators