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Bootstrapping Heisenberg magnets and their cubic instability

Chester, Shai M. and Landry, Walter and Liu, Junyu and Poland, David and Simmons-Duffin, David and Su, Ning and Vichi, Alessandro (2021) Bootstrapping Heisenberg magnets and their cubic instability. Physical Review D, 104 (10). Art. No. 105013. ISSN 2470-0010. doi:10.1103/PhysRevD.104.105013.

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We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O(3) singlet s, vector ϕ, and rank-2 symmetric tensor t. We determine their scaling dimensions to be (Δ_ϕ,Δ_s,Δ_t) = (0.518942(51), 1.59489(59), 1.20954(23)), and also bound various operator product expansion coefficients. We additionally introduce a new “tip-finding” algorithm to compute an upper bound on the leading rank-4 symmetric tensor t₄, which we find to be relevant with Δt₄ < 2.99056. The conformal bootstrap thus provides a numerical proof that systems described by the critical O(3) model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chester, Shai M.0000-0001-8803-1511
Liu, Junyu0000-0003-1669-8039
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Su, Ning0000-0001-5559-7922
Vichi, Alessandro0000-0001-6577-6887
Additional Information:© 2021 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. Funded by SCOAP3. Received 18 June 2021; accepted 3 September 2021; published 18 November 2021. We thank Yinchen He, Igor Klebanov, Filip Kos, Zhijin Li, João Penendones, Junchen Rong, Slava Rychkov, Andreas Stergiou, and Ettore Vicari for discussions. W. L., J. L., and D. S.-D. are supported by Simons Foundation Grant No. 488657 (Simons Collaboration on the Nonperturbative Bootstrap). D. S.-D. and J. L. are also supported by a DOE Early Career Award under Grant No. DE-SC0019085. D. P. is supported by Simons Foundation Grant No. 488651 (Simons Collaboration on the Nonperturbative Bootstrap) and DOE Grants No. DE-SC0020318 and No. DE-SC0017660. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 758903). A. V. is also supported by the Swiss National Science Foundation (SNSF) under Grant No. PP00P2-163670. S. M. C. is supported by a Zuckerman STEM Leadership Fellowship. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) Comet Cluster at the San Diego Supercomputing Center (SDSC) through allocation PHY190023, which is supported by National Science Foundation Grant No. ACI-1548562. This work also used the EPFL SCITAS cluster, which is supported by the SNSF Grant No. PP00P2-163670, the Caltech High Performance Cluster, partially supported by a grant from the Gordon and Betty Moore Foundation, and the Grace computing cluster, supported by the facilities and staff of the Yale University Faculty of Sciences High Performance Computing Center.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Department of Energy (DOE)DE-SC0019085
Simons Foundation488651
Department of Energy (DOE)DE-SC0020318
Department of Energy (DOE)DE-SC0017660
European Research Council (ERC)758903
Swiss National Science Foundation (SNSF)PP00P2-163670
Zuckerman STEM Leadership ProgramUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Yale UniversityUNSPECIFIED
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Issue or Number:10
Record Number:CaltechAUTHORS:20201203-155726059
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106903
Deposited By: Joy Painter
Deposited On:04 Dec 2020 22:14
Last Modified:18 Nov 2021 23:43

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