Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order

Abstract

Two-dimensional spin-orbital magnets with strong exchange frustration have recently been predicted to facilitate the realization of a quantum critical point in the Gross-Neveu-SO(3) universality class. In contrast to previously known Gross-Neveu-type universality classes, this quantum critical point separates a Dirac semimetal and a long-range-ordered phase, in which the fermion spectrum is only partially gapped out. Here, we characterize the quantum critical behavior of the Gross-Neveu-SO(3) universality class by employing three complementary field-theoretical techniques beyond their leading orders. We compute the correlation-length exponent $\nu$, the order-parameter anomalous dimension ${\eta }_{\varphi }$, and the fermion anomalous dimension ${\eta }_{\psi }$ using a three-loop $\epsilon$ expansion around the upper critical space-time dimension of four, a second-order large-$N$ expansion (with the fermion anomalous dimension obtained even at the third order), as well as a functional renormalization group approach in the improved local potential approximation. For the physically relevant case of $N=3$ flavors of two-component Dirac fermions in 2+1 space-time dimensions, we obtain the estimates $1/\nu =1.03(15)$, ${\eta }_{\varphi }=0.42(7)$, and ${\eta }_{\psi }=0.180(10)$ from averaging over the results of the different techniques, with the displayed uncertainty representing the degree of consistency among the three methods.

arXiv comment18 pages, 7 figures, 3 tables, 1 ancillary file "GNSO3-exponents.m". v2: additional explanations, minor corrections

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