Critical structure and emergent symmetry of Dirac fermion systems

Abstract

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order $\epsilon$ expansion in $4-\epsilon$ dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with $N_f$ flavors of four-component Dirac fermions coupled strongly to an $O(N)$ scalar field under a small $O(N)$-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general $N$ and $N_f$. Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for $N\ge 4$ on the basis of $O(N)$-GNY model. It turns out that the chiral emergent-$O(N)$ universality class is physically meaningful if and only if $N<2N_f+4$. On this premise, the small $O(N)$-symmetry breaking perturbation is always irrelevant in the chiral emergent-$O(N)$ universality class. Our studies show that the emergent symmetry in Dirac systems has an upper boundary $O(2N_f+3)$, depending on the flavor numbers $N_f$. As a result, the emergent-$O(4)$ and $O(5)$ symmetries are possible to be found in the systems with fermion flavor $N_f=1$, and the emergent-$O(4)$, $O(5)$, $O(6)$ and $O(7)$ symmetries are expected to be found in the systems with fermion flavor $N_f=2$. Our result also suggests some rich transitions with emergent-$Z_2\times O(2)\times O(3)$ symmetry and so on. Interestingly, in the emergent-$O(4)$ universality class, there is a supersymmetric critical point which is expected to be found in the systems with fermion flavor $N_f=1$.

14pages,6figures,1table

References in corpus (30)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological Mott Insulators
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry at a critical point of a lattice model
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Quantum superconducting criticality in graphene and topological insulators
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Four loop renormalization of the Gross-Neveu model
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Gauge-field-assisted Kekulé quantum criticality
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• TASI Lectures on the Higher Spin - CFT duality
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Competing nodal d-wave superconductivity and antiferromagnetism
• Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Critical exponent $\omega$ in the Gross-Neveu-Yukawa model at $O(1/N)$
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics