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Title: Bootstrapping MN and tetragonal CFTs in three dimensions

Abstract

Conformal field theories (CFTs) with MN and tetragonal global symmetry in d = 2 + 1 dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the ε = 4 – d expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-N expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the ε expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the ε expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups O(2)2 x S2 and O(2)3 x S3, a second kink is found. In the O(2)2 x S2 case it is argued to be saturated by a CFT that belongs to a new universality class relevant formore » the structural phase transition of NbO2 and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2)3 x S3 case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.« less

Authors:
ORCiD logo [1]
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Div.
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1573999
Report Number(s):
LA-UR-19-25903
Journal ID: ISSN 2542-4653
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2542-4653
Publisher:
SciPost Foundation
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Atomic; Nuclear and Particle Physics

Citation Formats

Stergiou, Andreas. Bootstrapping MN and tetragonal CFTs in three dimensions. United States: N. p., 2019. Web. doi:10.21468/SciPostPhys.7.1.010.
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Stergiou, Andreas. Bootstrapping MN and tetragonal CFTs in three dimensions. United States. https://doi.org/10.21468/SciPostPhys.7.1.010
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Stergiou, Andreas. Wed . "Bootstrapping MN and tetragonal CFTs in three dimensions". United States. https://doi.org/10.21468/SciPostPhys.7.1.010. https://www.osti.gov/servlets/purl/1573999.
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@article{osti_1573999,
title = {Bootstrapping MN and tetragonal CFTs in three dimensions},
author = {Stergiou, Andreas},
abstractNote = {Conformal field theories (CFTs) with MN and tetragonal global symmetry in d = 2 + 1 dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the ε = 4 – d expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-N expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the ε expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the ε expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups O(2)2 x S2 and O(2)3 x S3, a second kink is found. In the O(2)2 x S2 case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO2 and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2)3 x S3 case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.},
doi = {10.21468/SciPostPhys.7.1.010},
journal = {SciPost Physics},
number = 1,
volume = 7,
place = {United States},
year = {2019},
month = {7}
}
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