# 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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