{"title":"高维的安德森模型中的扩散","authors":"P. Prelovšek, J. Herbrych","doi":"10.1103/PhysRevB.103.L241107","DOIUrl":null,"url":null,"abstract":"We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites and we present results for diffusion in hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behaviour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.","PeriodicalId":8511,"journal":{"name":"arXiv: Strongly Correlated Electrons","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Diffusion in the Anderson model in higher dimensions\",\"authors\":\"P. Prelovšek, J. Herbrych\",\"doi\":\"10.1103/PhysRevB.103.L241107\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites and we present results for diffusion in hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behaviour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.\",\"PeriodicalId\":8511,\"journal\":{\"name\":\"arXiv: Strongly Correlated Electrons\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Strongly Correlated Electrons\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevB.103.L241107\",\"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: Strongly Correlated Electrons","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/PhysRevB.103.L241107","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
我们提出了一种扩展的微规范Lanczos方法(MCLM)，用于直接评估非相互作用粒子的无序安德森模型中的扩散常数及其频率依赖性。该方法允许研究超过$10^6$位的系统，我们给出了在$ d = 3- $ 7$维的超立方晶格中的扩散结果。在向局部化过渡的下面，我们确认了动态标度行为，我们感兴趣的是一个广泛的非相干扩散区域，类似于渗透现象和相互作用的多体局部化系统。
Diffusion in the Anderson model in higher dimensions
We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites and we present results for diffusion in hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behaviour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.
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