Bosonization of Fermi Liquids

We consider systems of non-relativistic, interacting electrons at finite density and zero temperature in d = 2, 3, ... 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 ”LutherHaldane” bosonization techniques. T RG calculations are organized as a double expansion in the inverse scale parameter, λ−1, which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant, gλ, which measures the strength of electron interactions at energy scales ∼ vF kF 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 λ−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 longrange, transverse, current-current interactions a deviation from LFL behaviour is possible : if the exponent α parametrizing the singularity of the interaction potential in momentum space by V̂ (|~ p|) ∼ 1 |~ p|α is greater than or equal to d− 1, the results of the bosonization calculation are consistent with a MFL.