A new renormalization group approach for systems with strong electron correlation

TL;DR

This paper introduces a novel renormalization group method that uses a magnetic field to suppress spin fluctuations, enabling perturbative calculations of low-energy properties in strongly correlated electron systems like the Anderson model.

Contribution

It presents a new approach that combines field-dependent perturbation theory with renormalization group flow to study strongly correlated systems without relying solely on non-perturbative methods.

Findings

The method accurately reproduces renormalized parameters for the Anderson model.

Flow of parameters matches results from numerical renormalization group and Bethe ansatz.

Approach provides a new way to analyze low-energy behavior in correlated electron systems.

Abstract

The anomalous low energy behaviour observed in metals with strong electron correlation, such as in the heavy fermion materials, is believed to arise from the scattering of the itinerant electrons with low energy spin fluctuations. In systems with magnetic impurities this scattering leads to the Kondo effect and a low energy renormalized energy scale, the Kondo temperature $T_{\rm K}$. It has been generally assumed that these low energy scales can only be accessed by a non-perturbative approach due to the strength of the local inter-electron interactions. Here we show that it is possible to circumvent this difficulty by first suppressing the spin fluctuations with a large magnetic field. As a first step field-dependent renormalized parameters are calculated using standard perturbation theory. A renormalized perturbation theory is then used to calculate the renormalized parameters for a reduced magnetic field strength. The process can be repeated and the flow of the renormalized parameters continued to zero magnetic field. We illustrate the viability of this approach for the single impurity Anderson model. The results for the renormalized parameters, which flow as a function of magnetic field, can be checked with those from numerical renormalization group and Bethe ansatz calculations.