Random translation-invariant Hamiltonians and their spectral gaps

@article{Jauslin2022RandomTH,
  title={Random translation-invariant Hamiltonians and their spectral gaps},
  author={Ian Jauslin and Marius Lemm},
  journal={Quantum},
  year={2022}
}
We consider random translation-invariant frustration-free quantum spin Hamiltonians on ZD in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result is that, under a small rank constraint, the Hamiltonians are automatically frustration-free and they are gapped with a positive probability. This extends previous results on 1D spin chains to all dimensions. The argument additionally controls the local gap. As an… 
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