Effective Soft-Mode Theory of Strongly Interacting Fermions

Abstract

An effective field theory for clean electron systems is developed in analogy to the generalized nonlinear sigma-model for disordered interacting electrons. The physical goal is to separate the soft or massless electronic degrees of freedom from the massive ones and integrate out the latter to obtain a field theory in terms of the soft degrees of freedom only. The resulting theory is not perturbative with respect to the electron-electron interaction. It is controlled by means of a systematic loop expansion and allows for a renormalization-group analysis in a natural way. It is applicable to universal phenomena within phases, and to transitions between phases, with order parameters in arbitrary angular-momentum channels, and in the spin-singlet, spin-triplet, particle-hole, and particle-particle channels. Applications include ferromagnetic and ferrimagnetic ordering, non-s-wave ferromagnetic order (magnetic nematics), Fermi-liquid to non-Fermi-liquid transitions, and universal phenomena within a Fermi-liquid phase.

28pp, 5 figs; version corrects typos and other minor mistakes, adds references

References in corpus (4)

• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Theory of a Fermi-Liquid-to-Non-Fermi-Liquid Quantum Phase Transition in Dimensions d>1
• Low energy excitations and singular contributions in the thermodynamics of clean Fermi liquids

Cited by in corpus (17)

• Metallic Quantum Ferromagnets
• Universal low-temperature tricritical point in metallic ferromagnets and ferrimagnets
• Disorder dependence of the ferromagnetic quantum phase transition
• A dynamical relation between dual finite temperature classical and zero temperature quantum systems: quantum critical jamming and quantum dynamical heterogeneities
• A unified theory of ferromagnetic quantum phase transitions in heavy fermion metals
• Nonanalyticities in a Strongly Correlated Fermi Liquid: Corrections to Scaling at the Fermi-Liquid Fixed Point
• Soft modes in Fermi liquids at arbitrary temperatures
• Fluctuating Quantum Kinetic Theory
• Soft Modes and Nonanalyticities in a Clean Dirac Metal
• An emerging global picture of heavy fermion physics
• Magnetic Quantum Phase Transitions in a Clean Dirac Metal
• The quantum ferromagnetic transition in a clean Kondo lattice is discontinuous
• Quantum Ferromagnetic Transition in Clean Dirac Metals
• Scaling Theory of a Compressibility-Driven Metal-Insulator Transition in a Two-Dimensional Electron Fluid
• Quantum Correlations in Metals that Grow in Time and Space
• Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals
• Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations