{"intvolume":"        93","publisher":"American Physical Society","abstract":[{"lang":"eng","text":"The many-body localization transition (MBLT) between ergodic and many-body localized phases in disordered interacting systems is a subject of much recent interest. The statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, a fractal enhancement of matrix elements upon approaching the MBLT from the delocalized side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interactions and the level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories."}],"publist_id":"6416","extern":1,"issue":"4","oa":1,"publication_status":"published","citation":{"mla":"Serbyn, Maksym, and Joel Moore. “Spectral Statistics across the Many-Body Localization Transition.” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 93, no. 4, American Physical Society, 2016, doi:<a href=\"https://doi.org/10.1103/PhysRevB.93.041424\">10.1103/PhysRevB.93.041424</a>.","ista":"Serbyn M, Moore J. 2016. Spectral statistics across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 93(4).","short":"M. Serbyn, J. Moore, Physical Review B - Condensed Matter and Materials Physics 93 (2016).","apa":"Serbyn, M., &#38; Moore, J. (2016). Spectral statistics 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.93.041424\">https://doi.org/10.1103/PhysRevB.93.041424</a>","ieee":"M. Serbyn and J. Moore, “Spectral statistics across the many-body localization transition,” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 93, no. 4. American Physical Society, 2016.","ama":"Serbyn M, Moore J. Spectral statistics across the many-body localization transition. <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2016;93(4). doi:<a href=\"https://doi.org/10.1103/PhysRevB.93.041424\">10.1103/PhysRevB.93.041424</a>","chicago":"Serbyn, Maksym, and Joel Moore. “Spectral Statistics across the Many-Body Localization Transition.” <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society, 2016. <a href=\"https://doi.org/10.1103/PhysRevB.93.041424\">https://doi.org/10.1103/PhysRevB.93.041424</a>."},"doi":"10.1103/PhysRevB.93.041424","author":[{"first_name":"Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","full_name":"Maksym Serbyn","orcid":"0000-0002-2399-5827"},{"first_name":"Joel","last_name":"Moore","full_name":"Moore, Joel E"}],"date_published":"2016-01-29T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1508.07293","open_access":"1"}],"day":"29","type":"journal_article","year":"2016","status":"public","publication":"Physical Review B - Condensed Matter and Materials Physics","date_created":"2018-12-11T11:49:33Z","date_updated":"2021-01-12T08:22:26Z","month":"01","volume":93,"quality_controlled":0,"_id":"986","title":"Spectral statistics across the many-body localization transition"}