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

TL;DR

This paper investigates a novel quantum critical point in spin-orbital liquids, characterized by fractionalized excitations, using advanced field-theoretical methods beyond leading order to provide precise critical exponents.

Contribution

It introduces a detailed analysis of the Gross-Neveu-SO(3) universality class with three complementary techniques, extending previous studies beyond leading order to improve accuracy of critical exponents.

Findings

Estimated critical exponents for N=3 flavors in 2+1D.

Demonstrated consistency among three different theoretical approaches.

Provided refined values for correlation-length and anomalous dimensions.

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 $\eta_\phi$, 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 $1/\nu = 1.03(15)$, $\eta_\phi = 0.42(7)$, 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.