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.
Abdul-Rahman, M
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Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.
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Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices
Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.