{"title":"On the critical finite-size gap scaling for frustration-free Hamiltonians","authors":"Marius Lemm, Angelo Lucia","doi":"arxiv-2409.09685","DOIUrl":null,"url":null,"abstract":"We prove that the critical finite-size gap scaling for frustration-free\nHamiltonians is of inverse-square type. The novelty of this note is that the\nresult is proved on general graphs and for general finite-range interactions.\nTherefore, the inverse-square critical gap scaling is a robust, universal\nproperty of finite-range frustration-free Hamiltonians. This places further\nlimits on their ability to produce conformal field theories in the continuum\nlimit. Our proof refines the divide-and-conquer strategy of Kastoryano and the\nsecond author through the refined Detectability Lemma of Gosset--Huang.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09685","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the critical finite-size gap scaling for frustration-free
Hamiltonians is of inverse-square type. The novelty of this note is that the
result is proved on general graphs and for general finite-range interactions.
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.
我们证明了无挫折哈密顿的临界有限大小间隙缩放是反平方类型的。因此,反平方临界间隙缩放是有限范围无挫折哈密顿的一个稳健而普遍的特性。这进一步限制了它们在连续极限中产生共形场论的能力。我们的证明完善了卡斯托里亚诺和第二作者的分而治之策略,即通过高塞特--黄的精炼可探测性训令(Detectability Lemma of Gosset--Huang)。