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From Bloch Oscillations to Many Body Localization in Clean Interacting Systems

van Nieuwenburg, Evert and Baum, Yuval and Refael, Gil (2019) From Bloch Oscillations to Many Body Localization in Clean Interacting Systems. Proceedings of the National Academy of Sciences of the United States of America, 116 (19). pp. 9269-9274. ISSN 0027-8424. PMCID PMC6511026. doi:10.1073/pnas.1819316116.

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In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier–Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.

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van Nieuwenburg, Evert0000-0003-0323-0031
Additional Information:© 2019 National Academy of Sciences. Published under the PNAS license. Edited by Angel Rubio, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany, and approved March 29, 2019 (received for review November 9, 2018). This work was supported by Swiss National Science Foundation Grant P2EZP2-172185 (to E.v.N.), Army Research Office Multidisciplinary University Research Initiative W911NF-16-1-0361, “Quantum Materials by Design with Electromagnetic Excitation,” sponsored by the US Army and the Packard Foundation (G.R.), and the Institute for Quantum Information and Matter, an NSF Physics Frontier Center funded in part by the Moore Foundation. Author contributions: E.v.N., Y.B., and G.R. designed research, performed research, analyzed data, and wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Data deposition: The C++ code developed for this work has been deposited in GitHub,, and the data for Fig. 3 have been deposited in CaltechData, This article contains supporting information online at
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)P2EZP2-172185
Army Research Office (ARO)W911NF-16-1-0361
David and Lucile Packard FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:many-body localization; Stark; thermalization; ergodicity
Issue or Number:19
PubMed Central ID:PMC6511026
Record Number:CaltechAUTHORS:20180821-144923153
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Official Citation:From Bloch oscillations to many-body localization in clean interacting systems. Evert van Nieuwenburg, Yuval Baum, Gil Refael. Proceedings of the National Academy of Sciences May 2019, 116 (19) 9269-9274; DOI: 10.1073/pnas.1819316116
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88991
Deposited By: Joy Painter
Deposited On:21 Aug 2018 22:43
Last Modified:16 Nov 2021 00:31

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