Corpus ID: 225102999

Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

@article{Nachtergaele2020QuasiLocalityBF,
  title={Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States},
  author={Bruno Nachtergaele and Robert Sims and Amanda Young},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi-Hastings-Michalakis (BHM) strategy that under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work we expand the class of frustration-free quantum… Expand

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References

SHOWING 1-10 OF 112 REFERENCES
Lie–Schwinger Block-Diagonalization and Gapped Quantum Chains
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of theExpand
Stability of Frustration-Free Hamiltonians
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 callExpand
Topological quantum order: Stability under local perturbations
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 ofExpand
A Short Proof of Stability of Topological Order under Local Perturbations
Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topologicalExpand
Anyons in an exactly solved model and beyond
A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions mayExpand
Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy densityExpand
Lieb-Schultz-Mattis in higher dimensions
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional spin systems is shown. The physical motivation for the result is that such spin systems typically either have long-rangeExpand
Locality in quantum and Markov dynamics on lattices and networks.
  • M. Hastings
  • Physics, Medicine
  • Physical review letters
  • 2004
TLDR
For a broad class of dynamics, it is proved that ground or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. Expand
Kitaev
  • Fault-tolerant quantum computation by anyons, Ann. Phys. 303
  • 2003
Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains
We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and RommelseExpand
...
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2
3
4
5
...