Bosonization of Fermi Liquids

TL;DR

This paper investigates the conditions under which interacting electron systems in two or more dimensions deviate from Landau Fermi liquid behavior, using renormalization group and bosonization methods to analyze the effects of different interaction types.

Contribution

It combines RG and bosonization techniques to characterize when electron systems exhibit Marginal Fermi liquid behavior beyond the Landau Fermi liquid fixed point.

Findings

Short-range interactions lead to Fermi liquid behavior.

Long-range density-density interactions also flow to Fermi liquid fixed point.

Long-range current-current interactions can produce Marginal Fermi liquid behavior when the interaction's singularity exponent exceeds a threshold.

Abstract

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 greater or equal than 2 . The interacting electron system is analyzed by combining renormalization group (RG) methods with bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter, $\lambda^{-1} ,$ which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant, $ g_\lambda , $ which measures the strength of electron interactions at corresponding energy scales. Excluding a superconducting instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of $ \lambda^{-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 behaviour is possible : the results of the bosonization calculation are consistent with a MFL, if the exponent parametrizing the singularity of the interaction potential in momentum space is greater than or equal to d-1.