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book part or chapter
Finite-size criteria for spectral gaps in 𝐷-dimensional quantum spin systems
2020
Contemporary Mathematics
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.
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Type
book part or chapter
Authors
Publication date
2020
Publisher
Published in
Contemporary Mathematics
ISBN of the book
978-1-4704-4841-7
Publisher place
Providence, Rhode Island
Start page
121
End page
132
Volume
741
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
October 1, 2020