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A learning algorithm with emergent scaling behavior for classifying phase transitions

Maskara, N. and Buchhold, M. and Endres, M. and van Nieuwenburg, E. (2021) A learning algorithm with emergent scaling behavior for classifying phase transitions. . (Unpublished)

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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, which is based on iteratively training convolutional networks of increasing complexity, and test it on the transverse field Ising chain and q = 6 Potts model. At the continuous Ising transition, we identify scaling behavior in the classification accuracy, from which we infer a characteristic classification length scale. It displays a power-law divergence at the critical point, with a scaling exponent that matches with the diverging correlation length. Our algorithm correctly identifies the thermodynamic phase of the system and extracts scaling behavior from projective measurements, independently of the basis in which the measurements are performed. Furthermore, we show the classification length scale is absent for the q=6 Potts model, which has a first order transition and thus lacks a divergent correlation length. The main intuition underlying our finding is that, for measurement patches of sizes smaller than the correlation length, the system appears to be at the critical point, and therefore the algorithm cannot identify the phase from which the data was drawn.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Buchhold, M.0000-0001-5194-9388
Endres, M.0000-0002-4461-224X
van Nieuwenburg, E.0000-0003-0323-0031
Additional Information:CC0 1.0 Universal (CC0 1.0) Public Domain Dedication. We thank Dolev Bluvstein, Dan Borgnia, Iris Cong, Brian Timar, and Ruben Verresen for insightful discussions. N.M. acknowledges funding from the Department of Energy Computational Science Graduate Fellowship under Award Number( s) DE-SC0021110. M.B. acknowledges funding via grant DI 1745/2-1 under DFG SPP 1929 GiRyd. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska- Curie grant agreement No. 847523 ‘INTERACTIONS’, and the Marie Sklodowksa-Curie grant agreement No. 895439 ‘ConQuER’.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0021110
Deutsche Forschungsgemeinschaft (DFG)DI 1745/2-1
Marie Curie Fellowship847523
Marie Curie Fellowship895439
Record Number:CaltechAUTHORS:20210412-082007992
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108688
Deposited By: Tony Diaz
Deposited On:12 Apr 2021 17:06
Last Modified:03 Jan 2022 22:53

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