Stability of Frustration-Free Hamiltonians

By Spyridon Michalakis, Justyna P. Zwolak. 2011

197 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4751ec0907b3654876118c48bc8d8b0e322eeada

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Arnau Riera
2. Martin Kliesch
3. Jens Eisert
4. Christian Gogolin

In Atomic and Molecular Physics, and Optics

1. Arnau Riera
2. Michael J. Kastoryano
3. Martin Kliesch
4. Jens Eisert
5. Christian Gogolin
6. Pasquale Calabrese
7. B. Doyon
8. Marcus Huber

Citations in the corpus

• Locality of temperature (2013, background): “A slightly different family of local topological quantum order conditions for closed quantum systems [41–44] has played a very important role in the theory of locally stable (topological) lattice systems and for rigorous proofs of entropic area laws.”