{"title":"多体定域态中的多重分形和fock空间定域:单粒子密度矩阵视角","authors":"Takahiro Orito, K. Imura","doi":"10.1103/PhysRevB.103.214206","DOIUrl":null,"url":null,"abstract":"Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_q$ is employed; it has been claimed that $D_q$ shows a jump from the delocalized value $D_q=1$ in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value $0<D_q<1$ at the ETH-MBL transition, yet exhibiting a conspicuous discrepancy from the fully localized value $D_q=0$, which indicate that multifractality remains inside the MBL phase. Here, to better quantify the situation we employ, instead of the commonly used computational basis, the one-particle density matrix (OPDM) and use its eigenstates (natural orbitals) as a Fock state basis for representing many-body eigenstates $|\\psi\\rangle$ of the system. Using this basis, we compute $D_q$ and other indices quantifying the Fock space localization, such as the local purity $S$, which is derived from the occupation spectrum $\\{n_\\alpha\\}$ (eigenvalues of the OPDM). We highlight the statistical distribution of Hamming distance $x_{\\mu\\nu}$ occurring in the pair-wise coefficients $|a_\\mu|^2|a_\\nu|^2$ in $S$, and compare this with a related quantity reported in the literature.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Multifractality and Fock-space localization in many-body localized states: One-particle density matrix perspective\",\"authors\":\"Takahiro Orito, K. Imura\",\"doi\":\"10.1103/PhysRevB.103.214206\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_q$ is employed; it has been claimed that $D_q$ shows a jump from the delocalized value $D_q=1$ in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value $0<D_q<1$ at the ETH-MBL transition, yet exhibiting a conspicuous discrepancy from the fully localized value $D_q=0$, which indicate that multifractality remains inside the MBL phase. Here, to better quantify the situation we employ, instead of the commonly used computational basis, the one-particle density matrix (OPDM) and use its eigenstates (natural orbitals) as a Fock state basis for representing many-body eigenstates $|\\\\psi\\\\rangle$ of the system. Using this basis, we compute $D_q$ and other indices quantifying the Fock space localization, such as the local purity $S$, which is derived from the occupation spectrum $\\\\{n_\\\\alpha\\\\}$ (eigenvalues of the OPDM). We highlight the statistical distribution of Hamming distance $x_{\\\\mu\\\\nu}$ occurring in the pair-wise coefficients $|a_\\\\mu|^2|a_\\\\nu|^2$ in $S$, and compare this with a related quantity reported in the literature.\",\"PeriodicalId\":8438,\"journal\":{\"name\":\"arXiv: Disordered Systems and Neural Networks\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Disordered Systems and Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevB.103.214206\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/PhysRevB.103.214206","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Multifractality and Fock-space localization in many-body localized states: One-particle density matrix perspective
Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_q$ is employed; it has been claimed that $D_q$ shows a jump from the delocalized value $D_q=1$ in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value $0
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