Journal
PHYSICAL REVIEW B
Volume 103, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.103.155160
Keywords
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [SFB 1143, 247310070, SFB 1238, 277146847]
- Emmy Noether program [JA2306/4-1, 411750675]
- DFG through a Mercator Fellowship
- Wurzburg-Dresden Cluster of Excellence ct.qmat [EXC 2147, 390858490]
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This study characterizes the quantum critical behavior of the Gross-Neveu-SO(3) universality class using three complementary field-theoretical techniques, and obtains estimates for the correlation-length exponent, order-parameter anomalous dimension, and fermion anomalous dimension. The results are obtained by averaging over different techniques and the uncertainty displayed represents the degree of consistency among the methods.
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.
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