Anomalous scaling of fermions and order parameter fluctuations at quantum criticality

Abstract

We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis approach since integrating out the fermions leads to a singular Landau-Ginzburg order parameter functional. We therefore derive and solve coupled renormalization group equations for the fermionic degrees of freedom and the bosonic order parameter fluctuations. In two spatial dimensions, fermions and bosons acquire anomalous scaling dimensions at the quantum critical point, associated with non-Fermi liquid behavior and non-Gaussian order parameter fluctuations.

8 pages, 9 figures, highlighted differences to Gross-Neveu model, updated version as published

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• The electronic properties of graphene
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Interactions and phase transitions on graphene's honeycomb lattice
• Relativistic Mott criticality in graphene
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Renormalization group theory of nematic ordering in d-wave superconductors
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
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Cited by in corpus (19)

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• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• On the Phase Structure of Many-Flavor QED${}_3$
• Quantum superconducting criticality in graphene and topological insulators
• UV fixed-point structure of the three-dimensional Thirring model
• Superconductivity of disordered Dirac fermions
• Ultracold atoms and the Functional Renormalization Group
• Quantum phase transitions in Dirac fermion systems
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Phase Diagram and Fixed-Point Structure of two dimensional N=1 Wess-Zumino Models
• Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals
• Competition between superconductivity and nematic order in high-$T_c$ superconductor
• Mass hierarchy in collective modes of pair-density-wave superconductors
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Superfluidity of Dirac Fermions in a Tunable Honeycomb Lattice: Cooper Pairing, Collective Modes, and Critical Currents
• Fermion-induced quantum critical point in the Landau-Devonshire model
• Anomalous criticality near semimetal-to-superfluid quantum phase transition in a two-dimensional Dirac cone model
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points