Corpus ID: 231924756

Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

@inproceedings{Nachtergaele2021StabilityOT,
  title={Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems},
  author={B. Nachtergaele and Robert Sims and Amanda Young},
  year={2021}
}
We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state. 
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References

SHOWING 1-10 OF 35 REFERENCES
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
The Stability of Free Fermi Hamiltonians
Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion HamiltoniansExpand
Automorphic equivalence within gapped phases in the bulk
We develop a new adiabatic theorem for unique gapped ground states which does not require the gap for local Hamiltonians. We instead require a gap in the bulk and a smoothness of expectation valuesExpand
Spectral gaps of frustration-free spin systems with boundary
In quantum many-body systems, the existence of a spectral gap above the ground state has far-reaching consequences. In this paper, we discuss "finite-size" criteria for having a spectral gap inExpand
Divide and conquer method for proving gaps of frustration free Hamiltonians
TLDR
It is proved that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\left(\frac{\log(n)^{2+\epsilon}}{n}\right)$ for any positive $\ep silon$. Expand
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
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
Local gap threshold for frustration-free spin systems
We improve Knabe's spectral gap bound for frustration-free translation-invariant local Hamiltonians in 1D. The bound is based on a relationship between global and local gaps. The global gap is theExpand
Improved local spectral gap thresholds for lattices of finite size
Knabe's theorem lower bounds the spectral gap of a one dimensional frustration-free local hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gapExpand
Adiabatic theorem in the thermodynamic limit. Part II: Systems with a gap in the bulk
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground stateExpand
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