Trace index and spectral flow in the entanglement spectrum of topological insulators
Abstract
We investigate the entanglement spectra of topological insulators, which manifest edge states on a lattice with spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the singleparticle entanglement spectrum, which we call a “trace index.” We find that any freefermion topological insulator that exhibits spectral flow has a nonvanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the singleparticle and manybody entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics.
 Publication:

Physical Review B
 Pub Date:
 November 2011
 DOI:
 10.1103/PhysRevB.84.195103
 arXiv:
 arXiv:1108.2907
 Bibcode:
 2011PhRvB..84s5103A
 Keywords:

 73.43.Cd;
 73.43.Nq;
 73.20.At;
 72.20.Dp;
 Theory and modeling;
 Quantum phase transitions;
 Surface states band structure electron density of states;
 General theory scattering mechanisms;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Other Condensed Matter
 EPrint:
 21 pages, 9 figures