--- _id: '6174' abstract: - lang: eng text: We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a “quantum avalanche.” We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the length scale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law-distributed in size. This points to the existence of a second transition within the MBL phase, at which these power laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent αc=2, and continuously varying exponents in the MBL phase consistent with the KT picture. article_number: '094205' article_processing_charge: No article_type: original author: - first_name: Philipp T. full_name: Dumitrescu, Philipp T. last_name: Dumitrescu - first_name: Anna full_name: Goremykina, Anna last_name: Goremykina - first_name: Siddharth A. full_name: Parameswaran, Siddharth A. last_name: Parameswaran - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 - first_name: Romain full_name: Vasseur, Romain last_name: Vasseur citation: ama: Dumitrescu PT, Goremykina A, Parameswaran SA, Serbyn M, Vasseur R. Kosterlitz-Thouless scaling at many-body localization phase transitions. Physical Review B. 2019;99(9). doi:10.1103/physrevb.99.094205 apa: Dumitrescu, P. T., Goremykina, A., Parameswaran, S. A., Serbyn, M., & Vasseur, R. (2019). Kosterlitz-Thouless scaling at many-body localization phase transitions. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.99.094205 chicago: Dumitrescu, Philipp T., Anna Goremykina, Siddharth A. Parameswaran, Maksym Serbyn, and Romain Vasseur. “Kosterlitz-Thouless Scaling at Many-Body Localization Phase Transitions.” Physical Review B. American Physical Society, 2019. https://doi.org/10.1103/physrevb.99.094205. ieee: P. T. Dumitrescu, A. Goremykina, S. A. Parameswaran, M. Serbyn, and R. Vasseur, “Kosterlitz-Thouless scaling at many-body localization phase transitions,” Physical Review B, vol. 99, no. 9. American Physical Society, 2019. ista: Dumitrescu PT, Goremykina A, Parameswaran SA, Serbyn M, Vasseur R. 2019. Kosterlitz-Thouless scaling at many-body localization phase transitions. Physical Review B. 99(9), 094205. mla: Dumitrescu, Philipp T., et al. “Kosterlitz-Thouless Scaling at Many-Body Localization Phase Transitions.” Physical Review B, vol. 99, no. 9, 094205, American Physical Society, 2019, doi:10.1103/physrevb.99.094205. short: P.T. Dumitrescu, A. Goremykina, S.A. Parameswaran, M. Serbyn, R. Vasseur, Physical Review B 99 (2019). date_created: 2019-03-25T07:32:08Z date_published: 2019-03-22T00:00:00Z date_updated: 2023-09-05T12:11:13Z day: '22' department: - _id: MaSe doi: 10.1103/physrevb.99.094205 external_id: arxiv: - '1811.03103' isi: - '000462883200001' intvolume: ' 99' isi: 1 issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1811.03103 month: '03' oa: 1 oa_version: Preprint publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Kosterlitz-Thouless scaling at many-body localization phase transitions type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 99 year: '2019' ...