Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions

Abstract

We study the renormalization group flow of the velocities in the field theory describing the coupling of the massless quasi-relativistic fermions to the bosons through the Yukawa coupling, as well as with both bosons and fermions coupled to a fluctuating $U(1)$ gauge field in two and three spatial dimensions. Different versions of this theory describe quantum critical behavior of interacting Dirac fermions in various condensed-matter systems. We perform an analysis using one-loop $\epsilon -$expansion about three spatial dimensions, which is the upper critical dimension in the problem. In two dimensions, we find that velocities of both charged fermions and bosons ultimately flow to the velocity of light, independently of the initial conditions, the number of fermionic and bosonic flavors, and the value of the couplings at the critical point. In three dimensions, due to the analyticity of the gauge field propagator, both the $U(1)$ charge and the velocity of light flow, which leads to a richer behavior than in two dimensions. We show that all three velocities ultimately flow to a common terminal velocity, which is non-universal and different from the original velocity of light. Therefore, emergence of the Lorentz symmetry in the ultimate infrared regime seems to be a rather universal feature of this class of theories in both two and three dimensions.

19 pages, 4 figures: Published version, added discussion, new references, typos corrected

References in corpus (13)

• Quantum Gravity at a Lifshitz Point
• Theory of interacting electrons on the honeycomb lattice
• Exciton condensation and charge fractionalization in a topological insulator film
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry at a critical point of a lattice model
• Quantum superconducting criticality in graphene and topological insulators
• Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials
• The emergence of a universal limiting speed
• Phase diagram of the Quantum Electrodynamics of 2D and 3D Dirac semimetals
• Mott multicriticality of Dirac electrons in graphene

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