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

• Published in: arXiv.org
• Main Authors: Shouryya Ray, Ihrig, Bernhard, Kruti, Daniel, Gracey, John A, Scherer, Michael M, Janssen, Lukas
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.04.2021
• Subjects: Critical point; Fermions; Field theory; Flavor (particle physics); Magnets; Mathematical analysis; Order parameters; Physics - High Energy Physics - Theory; Physics - Strongly Correlated Electrons; Relativity; Spacetime
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2101.10335

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.