A hierarchy of SDPs yields lower bounds on spectral gaps of frustration-free Hamiltonians that encompass and improve upon Knabe's bound on 1D spin chains.
Knabe, Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets, Journal of Sta- tistical Physics 52, 627 (1988)
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A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
A hierarchy of SDPs yields lower bounds on spectral gaps of frustration-free Hamiltonians that encompass and improve upon Knabe's bound on 1D spin chains.