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Title: Bootstrapping MN and tetragonal CFTs in three dimensions

Journal Article · · SciPost Physics
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Div.
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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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1573999
Report Number(s):
LA-UR-19-25903
Journal Information:
SciPost Physics, Vol. 7, Issue 1; ISSN 2542-4653
Publisher:
SciPost FoundationCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 20 works
Citation information provided by
Web of Science

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