Gaplessness is not generic for translation-invariant spin chains

@article{Lemm2019GaplessnessIN,
  title={Gaplessness is not generic for translation-invariant spin chains},
  author={Marius Lemm},
  journal={Physical Review B},
  year={2019}
}
  • M. Lemm
  • Published 28 February 2019
  • Physics
  • Physical Review B
The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movassagh, PRL 119 (2017), 220504] shows that a spatially random local quantum Hamiltonian is generically gapless. Here we observe that a gap is more common for translation-invariant quantum spin chains, more specifically, that these are gapped with a positive probability if the interaction is of small rank. This is in line… 
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