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Topological quantum order: Stability under local perturbations

- S. Bravyi, M. Hastings, S. Michalakis
- Mathematics
- 3 January 2010

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of… Expand

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

- S. Bachmann, S. Michalakis, B. Nachtergaele, Robert Sims
- Physics, Mathematics
- 4 February 2011

Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions… Expand

Non-local propagation of correlations in quantum systems with long-range interactions

- P. Richerme, Zhe-Xuan Gong,
+6 authors C. Monroe - PhysicsNature
- 10 July 2014

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Stability of Frustration-Free Hamiltonians

- S. Michalakis, Justyna P. Zwolak
- Physics, Mathematics
- 7 September 2011

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… Expand

Quantization of Hall Conductance for Interacting Electrons on a Torus

- M. Hastings, S. Michalakis
- Physics
- 5 June 2013

We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a… Expand

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement

- ChunJun Cao, S. Carroll, S. Michalakis
- Mathematics
- 27 June 2016

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor… Expand

Elementary excitations in gapped quantum spin systems.

- J. Haegeman, S. Michalakis, B. Nachtergaele, T. Osborne, N. Schuch, F. Verstraete
- PhysicsPhysical review letters
- 9 May 2013

TLDR

Stability of the Area Law for the Entropy of Entanglement

- S. Michalakis
- Physics
- 28 June 2012

Recent results on the stability of the spectral gap under general perturbations for frustration-free Hamiltonians, have motivated the following question: Does the entanglement entropy of quantum… Expand

Non-local propagation of correlations in long-range interacting quantum systems

- P. Richerme, Zhe-Xuan Gong,
+6 authors C. Monroe - Physics
- 20 January 2014

The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated [1–4] and how difficult the… Expand

Persistence of locality in systems with power-law interactions.

- Zhe-Xuan Gong, M. Foss-Feig, S. Michalakis, A. Gorshkov
- PhysicsPhysical review letters
- 23 January 2014

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