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

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.

17 pages; final version

References in corpus (5)

• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Quantitatively improved finite-size criteria for spectral gaps
• Random translation-invariant Hamiltonians and their spectral gaps
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Cited by in corpus (5)

• Rigorous lower bound on dynamical exponents in gapless frustration-free systems
• Rigorous lower bound of the dynamical critical exponent of the Ising model
• Quasi-local Frustration-Free Free Fermions
• Frustration-free free fermions and beyond
• Frustration-free free fermions