Rigorous Lower Bounds on Spectral Gaps of Frustration-Free Quantum Spin Chains
par
Amphithéâtre Léon Motchane
IHES
I will present some new results for obtaining rigorous lower bounds on the spectral gap of frustration-free quantum spin chains. Such spin chains are characterized by the fact that their ground state minimizes each local Hamiltonian term individually, and include paradigmatic models such as the AKLT and the Majumdar-Ghosh model. In my talk, I will discuss two new results, which significantly improve upon existing methods: First, a new approach based on semidefinite programming to obtain rigorous lower bounds on the spectral gap of frustration-free Hamiltonians. Second, a method based on the so-called "martingale method" of Fannes, Nachtergaele, and Werner, which not only significantly improves upon their method, but also results in a much simplified proof of the fact that a large class of frustration-free Hamiltonians (namely, parent Hamiltonians of well-conditioned Matrix Product States) are always gapped.
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Slava Rychkov