Bosonization of Fermi liquids

Abstract

We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d⩾2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\lambda }^{\mathrm{-}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\lambda }$ , which measures the strength of electron interactions at energy scales ∼${\mathrm{v}}_{\mathrm{F}}$ ${\mathrm{k}}_{\mathrm{F}}$ /λ. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\lambda }^{\mathrm{-}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent α parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)∼1/|p ${\mathrm{|}}^{\mathrm{\alpha }}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.