{"title":"Permutation Symmetry in Spin Adapted Many-Body Wave Functions","authors":"Maru Song, Ali Alavi, Giovanni Li Manni","doi":"10.1039/d4fd00061g","DOIUrl":null,"url":null,"abstract":"In the domain of exchange-coupled PNTM clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the CI eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, [(S<small><sup>(n)</sup></small>)<small><sup>2</sup></small>, H]. Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the distinct site permutations.","PeriodicalId":76,"journal":{"name":"Faraday Discussions","volume":null,"pages":null},"PeriodicalIF":3.3000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Faraday Discussions","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1039/d4fd00061g","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In the domain of exchange-coupled PNTM clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the CI eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, [(S(n))2, H]. Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the distinct site permutations.
在交换耦合 PNTM 簇领域,存在着局部新兴对称性,利用这些对称性可以大大提高此类系统的 CI 特征解的稀疏性。通过探索自旋适配多体基内的位点排列空间,可以揭示 CI 世俗问题的稀疏性;通过寻找最佳位点排序,可以产生高度压缩的波函数。然而,对于具有大量金属中心的集群来说,搜索排列空间的因子成本仍然是一个瓶颈。在这项工作中,我们结合了置换和点群对称性论证,并利用累积部分自旋和哈密顿算子[(S(n))2, H]之间的换向关系,探索了减少因子缩放的方法。某些位点排序会导致换向算子,从而产生更稀疏的波函数。我们将讨论两种图形策略,一种是快速评估感兴趣的换向算子,另一种是以树形搜索算法的形式预测有多少种不同的位点排列需要分析,从而消除排列空间中的冗余。特别有趣的是单子自旋态,可以利用额外的反转对称性来进一步减少不同位点的排列。