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

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