Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe
{"title":"对数正态Rosenzweig-Porter模型中的脆弱扩展相","authors":"Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe","doi":"10.1103/physrevresearch.2.043346","DOIUrl":null,"url":null,"abstract":"In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Fragile extended phases in the log-normal Rosenzweig-Porter model\",\"authors\":\"Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe\",\"doi\":\"10.1103/physrevresearch.2.043346\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.\",\"PeriodicalId\":8438,\"journal\":{\"name\":\"arXiv: Disordered Systems and Neural Networks\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Disordered Systems and Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevresearch.2.043346\",\"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/physrevresearch.2.043346","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fragile extended phases in the log-normal Rosenzweig-Porter model
In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.