[{"acknowledgement":"We   acknowledge   useful   discussions with V. Kravtsov, T. Grover, and R. Vasseur.  M.S. was supported by Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4307.  M.S. and D.A.  acknowledge  hospitality  of  KITP,  where  parts  of this work were completed (supported in part by the National Science Foundation under Grant No. NSF PHY11-25915)","external_id":{"isi":["000409429300004"]},"publist_id":"6814","article_processing_charge":"No","publication":"Physical Review B - Condensed Matter and Materials Physics","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Thouless energy and multifractality across the many-body localization transition","department":[{"_id":"MaSe"}],"status":"public","publisher":"American Physical Society","publication_identifier":{"issn":["24699950"]},"isi":1,"quality_controlled":"1","oa":1,"citation":{"ama":"Serbyn M, Zlatko P, Abanin D. Thouless energy and multifractality across the many-body localization transition. <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2017;96(10). doi:<a href=\"https://doi.org/10.1103/PhysRevB.96.104201\">10.1103/PhysRevB.96.104201</a>","mla":"Serbyn, Maksym, et al. “Thouless Energy and Multifractality across the Many-Body Localization Transition.” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 96, no. 10, 104201, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevB.96.104201\">10.1103/PhysRevB.96.104201</a>.","apa":"Serbyn, M., Zlatko, P., &#38; Abanin, D. (2017). Thouless energy and multifractality across the many-body localization transition. <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.96.104201\">https://doi.org/10.1103/PhysRevB.96.104201</a>","ista":"Serbyn M, Zlatko P, Abanin D. 2017. Thouless energy and multifractality across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 96(10), 104201.","short":"M. Serbyn, P. Zlatko, D. Abanin, Physical Review B - Condensed Matter and Materials Physics 96 (2017).","chicago":"Serbyn, Maksym, Papic Zlatko, and Dmitry Abanin. “Thouless Energy and Multifractality across the Many-Body Localization Transition.” <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevB.96.104201\">https://doi.org/10.1103/PhysRevB.96.104201</a>.","ieee":"M. Serbyn, P. Zlatko, and D. Abanin, “Thouless energy and multifractality across the many-body localization transition,” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 96, no. 10. American Physical Society, 2017."},"article_number":"104201","day":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1610.02389"}],"volume":96,"oa_version":"Submitted Version","doi":"10.1103/PhysRevB.96.104201","year":"2017","language":[{"iso":"eng"}],"month":"09","publication_status":"published","intvolume":"        96","type":"journal_article","date_updated":"2023-09-26T15:51:54Z","issue":"10","abstract":[{"lang":"eng","text":"Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this transition in two different models of disordered spin chains. We show that the behavior of matrix elements can be used to characterize the breakdown of thermalization and to extract the many-body Thouless energy. We find that upon increasing the disorder strength the system enters a critical region around the many-body localization transition. The properties of the system in this region are: (i) the Thouless energy becomes smaller than the level spacing, (ii) the matrix elements show critical dependence on the energy difference, and (iii) the matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. This critical region decreases with the system size, which we interpret as evidence for a diverging correlation length at the many-body localization transition. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values and shed light on the critical behavior near the many-body localization transition."}],"author":[{"full_name":"Serbyn, Maksym","first_name":"Maksym","last_name":"Serbyn","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zlatko, Papic","last_name":"Zlatko","first_name":"Papic"},{"full_name":"Abanin, Dmitry","last_name":"Abanin","first_name":"Dmitry"}],"date_published":"2017-09-06T00:00:00Z","scopus_import":"1","_id":"834","date_created":"2018-12-11T11:48:45Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"MaSe"}],"status":"public","title":"Noninteracting central site model localization and logarithmic entanglement growth","publisher":"American Physical Society","acknowledgement":"We  would  like  to  thank  Dmitry  Abanin,  Christophe  De\r\nBeule,  Joel  Moore,  Romain  Vasseur,  and  Norman  Yao  for\r\nmany  stimulating  discussions.  Financial  support  has  been\r\nprovided  by  the  Deutsche  Forschungsgemeinschaft  (DFG)\r\nvia Grant No. TR950/8-1, SFB 1170 “ToCoTronics” and the\r\nENB  Graduate  School  on  Topological  Insulators.  M.S.  was\r\nsupported by Gordon and Betty Moore Foundation’s EPiQS\r\nInitiative through Grant No. GBMF4307. F.P. acknowledges\r\nsupport from the DFG Research Unit FOR 1807 through Grant\r\nNo. PO 1370/2-1.","publist_id":"6955","publication":"Physical Review B","main_file_link":[{"url":"https://arxiv.org/abs/1701.02744","open_access":"1"}],"volume":96,"oa_version":"Submitted Version","publication_identifier":{"issn":["24699950"]},"quality_controlled":"1","oa":1,"citation":{"ista":"Hetterich D, Serbyn M, Domínguez F, Pollmann F, Trauzettel B. 2017. Noninteracting central site model localization and logarithmic entanglement growth. Physical Review B. 96(10), 104203.","ama":"Hetterich D, Serbyn M, Domínguez F, Pollmann F, Trauzettel B. Noninteracting central site model localization and logarithmic entanglement growth. <i>Physical Review B</i>. 2017;96(10). doi:<a href=\"https://doi.org/10.1103/PhysRevB.96.104203\">10.1103/PhysRevB.96.104203</a>","mla":"Hetterich, Daniel, et al. “Noninteracting Central Site Model Localization and Logarithmic Entanglement Growth.” <i>Physical Review B</i>, vol. 96, no. 10, 104203, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevB.96.104203\">10.1103/PhysRevB.96.104203</a>.","apa":"Hetterich, D., Serbyn, M., Domínguez, F., Pollmann, F., &#38; Trauzettel, B. (2017). Noninteracting central site model localization and logarithmic entanglement growth. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.96.104203\">https://doi.org/10.1103/PhysRevB.96.104203</a>","chicago":"Hetterich, Daniel, Maksym Serbyn, Fernando Domínguez, Frank Pollmann, and Björn Trauzettel. “Noninteracting Central Site Model Localization and Logarithmic Entanglement Growth.” <i>Physical Review B</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevB.96.104203\">https://doi.org/10.1103/PhysRevB.96.104203</a>.","ieee":"D. Hetterich, M. Serbyn, F. Domínguez, F. Pollmann, and B. Trauzettel, “Noninteracting central site model localization and logarithmic entanglement growth,” <i>Physical Review B</i>, vol. 96, no. 10. American Physical Society, 2017.","short":"D. Hetterich, M. Serbyn, F. Domínguez, F. Pollmann, B. Trauzettel, Physical Review B 96 (2017)."},"article_number":"104203","day":"13","publication_status":"published","intvolume":"        96","type":"journal_article","date_updated":"2021-01-12T08:12:35Z","doi":"10.1103/PhysRevB.96.104203","year":"2017","language":[{"iso":"eng"}],"month":"09","date_published":"2017-09-13T00:00:00Z","scopus_import":1,"_id":"724","date_created":"2018-12-11T11:48:09Z","issue":"10","author":[{"first_name":"Daniel","last_name":"Hetterich","full_name":"Hetterich, Daniel"},{"full_name":"Serbyn, Maksym","orcid":"0000-0002-2399-5827","last_name":"Serbyn","first_name":"Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Domínguez, Fernando","first_name":"Fernando","last_name":"Domínguez"},{"full_name":"Pollmann, Frank","first_name":"Frank","last_name":"Pollmann"},{"full_name":"Trauzettel, Björn","first_name":"Björn","last_name":"Trauzettel"}],"abstract":[{"lang":"eng","text":"We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. Although this coupling partially dilutes the Anderson localized peaks towards nearly resonant sites, the most weight of the original peaks remains unchanged. This leads to multifractal wave functions with a frozen spectrum of fractal dimensions, which is characteristic for localized phases in models with power-law hopping. Using a perturbative approach we identify two different dynamical regimes. At weak couplings to the central site, the transport of particles and information is logarithmic in time, a feature usually attributed to many-body localization. We connect such transport to the persistence of the Poisson statistics of level spacings in parts of the spectrum. In contrast, at stronger couplings the level repulsion is established in the entire spectrum, the problem can be mapped to the Fano resonance, and the transport is ballistic."}]}]