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 in a wide class of materials. 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. In the tetragonal case, no new kinks are found. Estimates for critical exponents are provided for a few cases describing phase transitions in various materials. In two particular MN cases, corresponding to theories with global symmetry groups $O(2{)}^2⋊S_2$ and $O(2{)}^3⋊S_3$, a second kink is found. In the $O(2{)}^2⋊S_2$ case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO${}_2$ and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the $O(2{)}^3⋊S_3$ 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.

arXiv comment20 pages, 7 figures. v2: Some experimental and $\epsilon$-expansion results added in the introduction. v3: Corrections regarding the applicability of our results to stacked triangular antiferromagnets. v4: Clarifications added. Applicability of our results to XY stacked triangular antiferromagnets reevaluated. v5: Further clarifying remarks added in Section 3

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