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arXiv:2101.10335 · Physical review. B./Physical review. B

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

Shouryya Ray, Bernhard Ihrig, Daniel Kruti, J. A. Gracey, Michael M. Scherer, Lukas Janssen

Published Apr 30, 2021• 20 citations
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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 $\ensuremath{\nu}$, the order-parameter anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, and the fermion anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}$ using a three-loop $\ensuremath{\epsilon}$ 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 $1/\ensuremath{\nu}=1.03(15), {\ensuremath{\eta}}_{\ensuremath{\phi}}=0.42(7)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.180(10)$ from averaging over the results of the different techniques, with the displayed uncertainty representing the degree of consistency among the three methods.

DOI
10.1103/physrevb.103.155160

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Evidence for relativistic quantum criticality of antiferromagnetism and superconductivity in two-dimensional Dirac fermion systems has been found in large-scale quantum Monte Carlo simulations. However, the corresponding (2+12+12+1)-dimensional Gross--Neveu--Yukawa field theory with Nf=2{N}_{f}=2Nf​=2 four-component Dirac fermions coupled to two triplets of order parameters does not exhibit a renormalization group fixed point at one-loop order. Instead, the theory only features a critical point for a large or very small fractional number of fermion flavors Nf{N}_{f}Nf​, which disappears for a broad range of flavor numbers around the physical case, Nf=2{N}_{f}=2Nf​=2, due to fixed-point annihilation. This raises the question on how to explain the observed scaling collapse in the quantum Monte Carlo data. Here, we extend previous renormalization-group analyses by studying a generalized model at two-loop order in $4\ensuremath{-}\ensuremath{\epsilon}$ spacetime dimensions. We determine the $\ensuremath{\epsilon}$ correction to the upper and lower critical flavor numbers for the fixed-point annihilation and find that they both go towards the physical case Nf=2{N}_{f}=2Nf​=2. However, this only happens very slowly, such that an extrapolation to $\ensuremath{\epsilon}=1$ still suggests the absence of criticality in 2+12+12+1 dimensions. Thereby, we consolidate the finding that the continuum field theory does not feature a stable renormalization-group fixed point and no true quantum criticality would be expected for the considered system. We briefly discuss a possible reconciliation in terms of a complex conformal field theory. Further, we also explore the fixed-point structure in an enlarged theory space and identify a candidate stable fixed-point solution.
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