Renormalization Group for Mixed Fermion-Boson Systems

Abstract

We formulate a momentum-shell renormalization group (RG) procedure that can be used in theories containing both bosons and fermions with a Fermi surface. We focus on boson-fermion couplings that are nearly forward-scattering, {\it i.e.} involving small momentum transfer ($\vec{q}\approx 0$) for the fermions. Special consideration is given to phase space constraints that result from the conservation of momentum and the imposition of ultraviolet cutoffs. For problems where the energy and momentum scale similarly (dynamic exponent $z=1$), we show that more than one formalism can be used and they give equivalent results. When the energy and momentum must scale differently ($z\ne 1$), the procedures available are more limited but a consistent RG scheme can still be formulated. Our approach is applicable to a variety of problems in condensed matter physics, such as itinerant-electron magnets and gauge fields interacting with fermions.

(v2) a few points made clearer and some types corrected

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Cited by in corpus (12)

• Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions
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• Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
• Non-Fermi liquid Superconductivity: Eliashberg versus the Renormalization Group
• Aspects of Renormalization in Finite Density Field Theory
• Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals
• Strange metal state near a heavy-fermion quantum critical point
• Strange superconductivity near an antiferromagnetic heavy fermion quantum critical point
• Magnon Bose-Einstein Condensation and Superconductivity in a Frustrated Kondo Lattice
• Enhanced Pairing of Quantum Critical Metals Near d=3+1
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons
• One-loop renormalization group study of boson-fermion mixtures