On the critical finite-size gap scaling for frustration-free Hamiltonians

• URL: http://arxiv.org/abs/2409.09685v2
• Date: Sat, 07 Jun 2025 11:00:52 GMT
• Title: On the critical finite-size gap scaling for frustration-free Hamiltonians
• Abstract summary: We prove that the critical finite-size gap scaling for frustration-free Hamiltonians is of inverse-square type.<n>This places further limits on their ability to produce conformal field theories in the continuum limit.
• Score: 0.30693357740321775
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathbb R^D$ 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.

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