Wilson-Fisher fixed points in presence of Dirac fermions

Abstract

Wilson-Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the ${\varphi }^4$ field theories that describe low-energy physics of the canonical models such as Ising, XY, and Heisenberg. Here I review its application to a class of the Gross-Neveu-Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the ${\varphi }^4$ field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term, and which still exhibit critical fixed points in the suitably formulated Wilson-Fisher $\epsilon$-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art $\epsilon$-expansion, quantum Monte Carlo, large-N, and functional renormalization group calculations can be made.

arXiv comment8 pages, Chapter for "50 years of the renormalization group/Dedicated to the memory of Michael E. Fisher", edited by A. Aharony, O. Entin-Wohlman, D. Huse, and L. Radzihovsky

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Cited by in corpus (10)

• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Twist-tuned quantum criticality in moiré bilayer graphene
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Boundary criticality for the Gross-Neveu-Yukawa models
• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Instabilities of a Generalized Gross-Neveu Quantum Criticality