Citation: Michalakis, Spyridon, and Justyna P. Zwolak. "Stability of frustration-free Hamiltonians." Communications in Mathematical Physics 322 (2013): 277-302.
Web: https://arxiv.org/abs/1109.1588
Tags: MTC-reconstruction, Lieb-Robinson
In this paper, the authors introduce a notion of "Local Topological Quantum Order" (LTQO). They then use this notion along with a local gap condition to prove a stability result under perturbations. The definition of LTQO generalizes the notion of TQO introduced in
> Bravyi, Sergey, Matthew B. Hastings, and Spyridon Michalakis. "Topological quantum order: stability under local perturbations." Journal of mathematical physics 51.9 (2010).
In the case that the relevant Hamiltonian is commuting and the decaying function Delta(l) is zero after some threshold, the definition of LTQO is the same as the definition of TQO in Bravyi et al.
This paper demonstrates good progress on the problem of properly defining topological order and showing that it is indeed a robust notion. The main technical tool used in the proof is spectral flow, based on the Lieb-Robinson bound.