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Fixed Points of Wegner-Wilson Flows and Many-Body Localization

Pekker, David and Clark, Bryan K. and Oganesyan, Vadim and Refael, Gil (2017) Fixed Points of Wegner-Wilson Flows and Many-Body Localization. Physical Review Letters, 119 (7). Art. No. 075701. ISSN 0031-9007. doi:10.1103/PhysRevLett.119.075701.

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Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner-Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a Gaussian white-noise-like distribution in the ergodic phase, a 1/f law inside the MBL phase, and scale-free distributions in the transition regime.

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Additional Information:© 2017 American Physical Society. Received 25 August 2016; published 16 August 2017. We are grateful to A. Scardicchio, S. Kehrein, E. Kapit, A. Chandran, D. Huse, V. Khemani, B. Altshuler, L. Rademaker, M. Ortuño, and X. Yu for stimulating discussions. D. P. acknowledges support from the Charles E. Kaufman foundation. B. K. C. was supported by the SciDAC program of the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-FG02-12ER46875. G. R. is grateful for support from the Institute of Quantum Information and Matter, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, and the Packard foundation. V. O. acknowledges support from the NSF DMR Grants Nos. 0955714 and 1508538. Parts of this work were performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293 (D. P., B. K. C., G. R., and V. O.), ICTP Trieste (V. O.), and KITP Santa Barbara, which is supported by National Science Foundation under Grant No. NSF PHY11-25915 (D.P, G. R., and V. O.). The authors thank all three centers for the hospitality offered to us. This research is part of the Blue Waters sustained petascale computing project, which is supported by the National Science Foundation (Awards OCI-0725070 and ACI-1238993) and the State of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana Champaign and its National Center for Supercomputing Applications.
Group:Institute for Quantum Information and Matter
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Charles E. Kaufman FoundationUNSPECIFIED
Department of Energy (DOE)DE-FG02-12ER46875
Institute of Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
State of IllinoisUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20170817-073043882
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80545
Deposited By: Tony Diaz
Deposited On:17 Aug 2017 15:05
Last Modified:15 Nov 2021 19:36

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