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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 (2020) Bootstrapping Heisenberg Magnets and their Cubic Instability. . (Unpublished)

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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 CFT 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 (Δs,Δϕ,Δt)=(0.518942(51),1.59489(59),1.20954(23)), and also bound various OPE 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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Liu, Junyu0000-0003-1669-8039
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:We thank Yinchen He, Igor Klebanov, Filip Kos, Zhijin Li, João Penendones, Junchen Rong, Slava Rychkov, Andreas Stergiou, and Ettore Vicari for discussions. WL, JL, and DSD are supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap). DSD and JL are also supported by a DOE Early Career Award under grant no. DE-SC0019085. DP is supported by Simons Foundation grant 488651 (Simons Collaboration on the Nonperturbative Bootstrap) and DOE grants DE-SC0020318 and 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). AV is also supported by the Swiss National Science Foundation (SNSF) under grant no. PP00P2-163670. SMC 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 number ACI-1548562. This work also used the EPFL SCITAS cluster, which is supported by the SNSF grant 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
Swiss National Science Foundation (SNSF)PP00P2-163670
European Research Council (ERC)758903
Zuckerman STEM Leadership ProgramUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
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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:04 Dec 2020 22:14

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