Renormalization-group approach to interacting fermions
- Sloane Laboratory of Physics, Yale University, New Haven, Connecticut 06520 (United States)
The stability or lack thereof of nonrelativistic fermionic systems to interactions is studied within the renormalization-group (RG) framework, in close analogy with the study of critical phenomena using [phi][sup 4] scalar field theory. A brief introduction to [phi][sup 4] theory in four dimensions and the path-integral formulation for fermions is given before turning to the problem at hand. As for the latter, the following procedure is used. First, the modes on either side of the Fermi surface within a cutoff [Lambda] are chosen for study, in analogy with the modes near the origin in [phi][sup 4] theory, and a path integral is written to describe them. Next, an RG transformation that eliminates a part of these modes, but preserves the action of the noninteracting system, is identified. Finally the possible perturbations of this free-field fixed point are classified as relevant, irrelevant or marginal. A [ital d]=1 warmup calculation involving a system of fermions shows how, in contrast to mean-field theory, which predicts a charge-density wave for arbitrarily weak repulsion, and superconductivity for arbitrarily weak attraction, the renormalization-group approach correctly yields a scale-invariant system (Luttinger liquid) by taking into account both instabilities.
- OSTI ID:
- 5119703
- Journal Information:
- Reviews of Modern Physics; (United States), Vol. 66:1; ISSN 0034-6861
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FERMIONS
RENORMALIZATION
CORRELATION FUNCTIONS
FERMI GAS
FERMI LEVEL
FEYNMAN PATH INTEGRAL
MEAN-FIELD THEORY
PERTURBATION THEORY
ROTATIONAL INVARIANCE
SCALAR FIELDS
SCALE INVARIANCE
STABILITY
ENERGY LEVELS
FLUIDS
FUNCTIONS
GASES
INTEGRALS
INVARIANCE PRINCIPLES
665430* - Other Topics in Quantum Fluids & Solids- (1992-)
662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)