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

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Helical Metal Inside a Topological Band Insulator
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators