{"title":"在半经典近似框架内研究量子相变的纠缠熵方法:测试其在卡斯滕三角形中的有效性","authors":"","doi":"10.1016/j.nuclphysa.2024.122960","DOIUrl":null,"url":null,"abstract":"<div><p>The entanglement entropy of <em>s</em> and <em>d</em> bosons in the framework of Interacting Boson Model -1 (IBM-1) has been obtained using consistent-Q formalism and semiclassical approximation. This has been possible by using Schmidt decomposition and expressing <em>s</em> and <em>d</em> bosons entanglement entropy in terms of Schmidt numbers. In this research, a simple method in the framework of IBM-1 has been presented for deriving the entanglement entropy in the Casten triangle. The results indicated that the entanglement entropy is sensitive to the shape-phase transition in the various regions of the Casten triangle. It was demonstrated that the entanglement entropy of <em>s</em> and <em>d</em> bosons in the semiclassical approximation depends only on the values of the deformation parameter (<em>β</em>) and is independent of the angular parameter (<em>γ</em>). Also, the entanglement entropy between <em>s</em> and <em>d</em> bosons reaches its maximum value in the <span><math><mi>O</mi><mo>(</mo><mn>6</mn><mo>)</mo></math></span> limit, while it decreases in the <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> limit, and reaches zero in the <span><math><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></span> limit. Based on the results obtained via Schmidt decomposition, it is shown that the probability distribution functions of the number of <em>s</em> bosons in IBM-1 are the binomial distributions. For <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>≫</mo><mn>1</mn></math></span>, it was proved that the distribution function in the <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mn>6</mn><mo>)</mo></math></span> and <span><math><mover><mrow><mi>S</mi><mi>U</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow><mo>‾</mo></mover></math></span> limits is the Gaussian, and in the <span><math><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></span> limit is the Poissonian.</p></div>","PeriodicalId":19246,"journal":{"name":"Nuclear Physics A","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0375947424001428/pdfft?md5=9c586631e41302b09f08ceee65702562&pid=1-s2.0-S0375947424001428-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Entanglement entropy approach for examining quantum phase transition in the framework of semiclassical approximation: Testing its validity in Casten triangle\",\"authors\":\"\",\"doi\":\"10.1016/j.nuclphysa.2024.122960\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The entanglement entropy of <em>s</em> and <em>d</em> bosons in the framework of Interacting Boson Model -1 (IBM-1) has been obtained using consistent-Q formalism and semiclassical approximation. This has been possible by using Schmidt decomposition and expressing <em>s</em> and <em>d</em> bosons entanglement entropy in terms of Schmidt numbers. In this research, a simple method in the framework of IBM-1 has been presented for deriving the entanglement entropy in the Casten triangle. The results indicated that the entanglement entropy is sensitive to the shape-phase transition in the various regions of the Casten triangle. It was demonstrated that the entanglement entropy of <em>s</em> and <em>d</em> bosons in the semiclassical approximation depends only on the values of the deformation parameter (<em>β</em>) and is independent of the angular parameter (<em>γ</em>). Also, the entanglement entropy between <em>s</em> and <em>d</em> bosons reaches its maximum value in the <span><math><mi>O</mi><mo>(</mo><mn>6</mn><mo>)</mo></math></span> limit, while it decreases in the <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> limit, and reaches zero in the <span><math><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></span> limit. Based on the results obtained via Schmidt decomposition, it is shown that the probability distribution functions of the number of <em>s</em> bosons in IBM-1 are the binomial distributions. For <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>≫</mo><mn>1</mn></math></span>, it was proved that the distribution function in the <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mn>6</mn><mo>)</mo></math></span> and <span><math><mover><mrow><mi>S</mi><mi>U</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow><mo>‾</mo></mover></math></span> limits is the Gaussian, and in the <span><math><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></span> limit is the Poissonian.</p></div>\",\"PeriodicalId\":19246,\"journal\":{\"name\":\"Nuclear Physics A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0375947424001428/pdfft?md5=9c586631e41302b09f08ceee65702562&pid=1-s2.0-S0375947424001428-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nuclear Physics A\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0375947424001428\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, NUCLEAR\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375947424001428","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 0
摘要
利用一致-Q 形式主义和半经典近似,我们得到了在相互作用玻色子模型-1(IBM-1)框架内 s 和 d 玻色子的纠缠熵。这是通过使用施密特分解和用施密特数表达 s 和 d 玻色子纠缠熵实现的。在这项研究中,提出了一种在 IBM-1 框架内推导卡斯滕三角形纠缠熵的简单方法。结果表明,纠缠熵对卡斯滕三角形各区域的形相转变非常敏感。研究证明,在半经典近似中,s 和 d 玻色子的纠缠熵只取决于形变参数(β)的值,而与角度参数(γ)无关。此外,s玻色子和d玻色子之间的纠缠熵在O(6)极限达到最大值,而在SU(3)极限下降,在U(5)极限为零。根据施密特分解得到的结果,IBM-1 中 s玻色子数量的概率分布函数是二项分布。对于 NB≫1,证明了其在 SU(3)、O(6)和 SU(3)‾ 极限的分布函数是高斯分布,而在 U(5) 极限的分布函数是泊松分布。
Entanglement entropy approach for examining quantum phase transition in the framework of semiclassical approximation: Testing its validity in Casten triangle
The entanglement entropy of s and d bosons in the framework of Interacting Boson Model -1 (IBM-1) has been obtained using consistent-Q formalism and semiclassical approximation. This has been possible by using Schmidt decomposition and expressing s and d bosons entanglement entropy in terms of Schmidt numbers. In this research, a simple method in the framework of IBM-1 has been presented for deriving the entanglement entropy in the Casten triangle. The results indicated that the entanglement entropy is sensitive to the shape-phase transition in the various regions of the Casten triangle. It was demonstrated that the entanglement entropy of s and d bosons in the semiclassical approximation depends only on the values of the deformation parameter (β) and is independent of the angular parameter (γ). Also, the entanglement entropy between s and d bosons reaches its maximum value in the limit, while it decreases in the limit, and reaches zero in the limit. Based on the results obtained via Schmidt decomposition, it is shown that the probability distribution functions of the number of s bosons in IBM-1 are the binomial distributions. For , it was proved that the distribution function in the , and limits is the Gaussian, and in the limit is the Poissonian.
期刊介绍:
Nuclear Physics A focuses on the domain of nuclear and hadronic physics and includes the following subsections: Nuclear Structure and Dynamics; Intermediate and High Energy Heavy Ion Physics; Hadronic Physics; Electromagnetic and Weak Interactions; Nuclear Astrophysics. The emphasis is on original research papers. A number of carefully selected and reviewed conference proceedings are published as an integral part of the journal.