Divide and conquer method for proving gaps of frustration free Hamiltonians

Research output: Contribution to journalJournal articlepeer-review

  • Michael J. Kastoryano
  • Angelo Lucia
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap. Thanks to this equivalence, we can prove 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 $\epsilon$.
Original languageEnglish
Article number033105
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2018
Pages (from-to)1-23
ISSN1742-5468
DOIs
Publication statusPublished - 2018

Bibliographical note

26 pages, 3 figures

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