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.
Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
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abstract
We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the {ground state of our model is non-degenerate and exhibits} a novel quantum phase transition from bounded entanglement entropy to a massively entangled state with volume entropy scaling. The ground state may be interpreted as a deformation away from the uniform superposition of colored Motzkin paths, showed by Movassagh and Shor to have a large (square-root) but sub-extensive scaling of entanglement into a state with an extensive entropy.
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2024 1verdicts
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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.