{"title":"Some Details Concerning Transition from the Hubbard Model to the Heisenberg Model","authors":"Dorota Jakubczyk","doi":"10.1016/S0034-4877(22)00080-5","DOIUrl":null,"url":null,"abstract":"<div><p><span>In this paper we present the example the details of the transition of the Hubbard model to the Heisenberg model in the limit of on-site repulsion constant </span><em>u</em><span> → ∞. We explore the models with respect to the nearest and the next-nearest-neighbour hopping. We construct the next-nearest-neighbour hopping free subspaces for the considered example and find the procedure applicable to any number and any configuration of electrons in the chain. We found that some eigenvalues permute themselves for a specific value of the ratio of on-site repulsion constant to hopping constant and the effect is more visible the greater the next-nearest-neighbour hopping is. A similar situation occurs for eigenvectors<span>. We also confirm SU(2)× SU(2) symmetry breaking when the next-nearest-neighbour hopping are considered.</span></span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"90 3","pages":"Pages 347-356"},"PeriodicalIF":1.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487722000805","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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Abstract
In this paper we present the example the details of the transition of the Hubbard model to the Heisenberg model in the limit of on-site repulsion constant u → ∞. We explore the models with respect to the nearest and the next-nearest-neighbour hopping. We construct the next-nearest-neighbour hopping free subspaces for the considered example and find the procedure applicable to any number and any configuration of electrons in the chain. We found that some eigenvalues permute themselves for a specific value of the ratio of on-site repulsion constant to hopping constant and the effect is more visible the greater the next-nearest-neighbour hopping is. A similar situation occurs for eigenvectors. We also confirm SU(2)× SU(2) symmetry breaking when the next-nearest-neighbour hopping are considered.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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