Bootstrapping Heisenberg magnets and their cubic instability

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Bootstrapping Heisenberg magnets and their cubic instability

Shai M. Chester, Walter Landry, Junyu Liu, David Poland, David Simmons-Duffin, Ning Su, and Alessandro Vichi

Phys. Rev. D 104, 105013 – Published 18 November 2021

Abstract

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 $t_{4}$ , which we find to be relevant with $Δ_{t_{4}} < 2.99056$ . 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.

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Received 18 June 2021
Accepted 3 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.105013

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Renormalization

Conformal symmetry

Conformal field theory Critical exponents Critical phenomena

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Shai M. Chester

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Herzl street 234, Rehovot, zip code 76100, Israel

Walter Landry

Simons Collaboration on the Nonperturbative Bootstrap and Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA

Junyu Liu

Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA and Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA

David Poland

Department of Physics, Yale University, New Haven, Connecticut 06520, USA

David Simmons-Duffin

Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA

Ning Su

Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and Department of Physics, University of Pisa, I-56127 Pisa, Italy

Alessandro Vichi

Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and Department of Physics, University of Pisa, I-56127 Pisa, Italy

Article Text

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Issue

Vol. 104, Iss. 10 — 15 November 2021

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