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Learning algorithm reflecting universal scaling behavior near phase transitions

Maskara, N. and Buchhold, M. and Endres, M. and van Nieuwenburg, E. (2022) Learning algorithm reflecting universal scaling behavior near phase transitions. Physical Review Research, 4 (2). Art. No. L022032. ISSN 2643-1564. doi:10.1103/physrevresearch.4.l022032.

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Machine-learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, “neural network scaling,” which is based on iteratively training convolutional networks of increasing (spatial) complexity and test it on the transverse field Ising chain and q = 6 Potts model. At the continuous Ising transition, our scaling procedure directly reflects the hallmark of a continuous (second-order) phase transition, divergence of a characteristic length scale. Specifically, we extract a classification length scale by measuring the response of the classification accuracy while varying the largest convolution size (architecture of the network). We observe empirically the scaling exponent of the classification length is consistent with a power law with the correlation length exponent ν = 1. Furthermore, we demonstrate the versatility of our algorithm by showing the universal scaling behaviors persist across a variety of measurement bases, including when the order parameter is nonlocal. Finally, we show that the classification length scale remains finite for the q = 6 Potts model, which has a first-order transition and lacks a divergent correlation length.

Item Type:Article
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URLURL TypeDescription Information
Maskara, N.0000-0001-5775-9542
Buchhold, M.0000-0001-5194-9388
Endres, M.0000-0002-4461-224X
van Nieuwenburg, E.0000-0003-0323-0031
Additional Information:© 2022 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 12 April 2021; revised 14 December 2021; accepted 15 February 2022; published 9 May 2022) We thank Dolev Bluvstein, Dan Borgnia, Soonwon Choi, Iris Cong, Mikahil Lukin, Brian Timar, Minh Tran, and Ruben Verresen for insightful discussions. N.M. acknowledges funding from a Department of Energy Computational Science Graduate Fellowship under Award No. DE-SC0021110. M.B. acknowledges funding from DFG via Grant No. DI 1745/2-1 under DFG SPP 1929 GiRyd and the CRC network TR 183 (project grant 277101999) as part of project B01. This project has received funding from the European Union's Horizon 2020 Research and Innovation Program under Marie Sklodowska-Curie Grant Agreement No. 847523 INTERACTIONS and Marie Sklodowksa-Curie Grant Agreement No. 895439 “ConQuER.”
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0021110
Deutsche Forschungsgemeinschaft (DFG)DI 1745/2-1
Deutsche Forschungsgemeinschaft (DFG)277101999
Marie Curie Fellowship847523
Marie Curie Fellowship895439
Issue or Number:2
Record Number:CaltechAUTHORS:20220601-257666000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114984
Deposited By: George Porter
Deposited On:02 Jun 2022 17:44
Last Modified:02 Jun 2022 17:44

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