Local-TQO and Stability of Frustration-Free Hamiltonians

The attention of the condensed matter and mathematical physics communities has recently focused on Hamiltonians with low-energy sectors exhibiting some form of topological order. In our work [1], we present a generalization of the result of Bravyi et al. [2,3] on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. In particular, the commutativity condition can be removed: We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. Also, we will discuss the ``Local Topological Quantum Order'' and ``Local-Gap'' conditions sufficient for proving stability. \\[4pt] [1] S. Michalakis and J. Pytel, {\em Stability of Frustration-Free Hamiltonians.} arXiv:1109.1588 (2011).\\[0pt] [2] S. Bravyi and M.B. Hastings, {\em A short proof of stability of topological order under local perturbations.} arXiv:1001.4363. \\[0pt] [3] S. Bravyi, M.B. Hastings, and S. Michalakis, {\em Topological quantum order: stability under local perturbations.} J. Math. Phys. {\bf 51}, 093512 (2010).