Communications in Mathematical Physics

, Volume 322, Issue 2, pp 277–302

Stability of Frustration-Free Hamiltonians

Article

DOI: 10.1007/s00220-013-1762-6

Cite this article as:
Michalakis, S. & Zwolak, J.P. Commun. Math. Phys. (2013) 322: 277. doi:10.1007/s00220-013-1762-6

Abstract

We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call Local Topological Quantum Order and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al. on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Quantum Information and Matter, CaltechPasadenaUSA
  2. 2.Department of PhysicsNicolaus Copernicus UniversityTorunPoland
  3. 3.Department of PhysicsOregon State UniversityCorvallisUSA

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