## Finite-size criteria for spectral gaps in 𝐷-dimensional quantum spin systems

We generalize the existing finite-size criteria for spectral gaps offrustration-free spin systems to D>2 dimensions. We obtain a local gapthreshold of 3/n, independent of D, for nearest-neighbor interactions. The 1/n scaling persists for arbitrary finite-range interactions in Z3. The key observation is that there is more flexibility in Knabe’s combinatorial approach if one employs the operator Cauchy-Schwarz inequality.

Published in:
Contemporary Mathematics, 741, 121-132
Year:
2020
Publisher:
Providence, Rhode Island, American Mathematical Society
ISBN:
978-1-4704-4841-7
Laboratories: