On the critical finite-size gap scaling for frustration-free Hamiltonians
arXiv:2409.09685 · doi:10.1142/S0129055X25500151
Abstract
We prove that the critical finite-size gap scaling for frustration-free Hamiltonians is of inverse-square type. The result covers general graphs embedded in and general finite-range interactions without requiring assumptions about the ground state correlations. Therefore, the inverse-square critical gap scaling is a robust, universal property of finite-range frustration-free Hamiltonians. This places further limits on their ability to produce conformal field theories in the continuum limit. Our proof refines the divide-and-conquer strategy of Kastoryano and the second author through the refined Detectability Lemma of Gosset--Huang.
arXiv comment17 pages; final version
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