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Physical Review Letters

Study of two magnetic impurities in a Fermi gas

Barbara Jones, C. M. Varma

Published Mar 2, 1987• 296 citations
Publisher

Abstract

The problem of two magnetic moments in a Fermi gas is studied with the numerical renormalization group used by Wilson for the Kondo problem. Even when the interaction energy of the moments is much smaller than the Kondo energy, the asymptotic low-temperature behavior is that of a correlated Kondo effect. An effective Hamiltonian for the low-temperature properties, which are nonuniversal, is deduced.

DOI
10.1103/physrevlett.58.843

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•Jan 1, 1998•2 citations
The problem of two magnetic moments in a Fermi gas is studied with the numerical renormalization group used by Wilson for the Kondo problem. Even when the interaction energy of the moments is much smaller than the Kondo energy, the asymptotic low-temperature behavior is that of a correlated Kondo effect. An effective Hamiltonian for the low-temperature properties, which are nonuniversal, is deduced.
The two-channel Kondo Hamiltonian has recently been proposed as a description of several experimental systems. Our numerical renormalization-group treatment of a pair of magnetic impurities shows that at low temperatures, interimpurity interactions destabilize the ``marginal-Fermi-liquid'' behavior predicted by a single-impurity model. We find four stable zero-temperature regimes, three of which can be described by Fermi-liquid theory. The fourth possesses a complex many-body ground state and non-Fermi-liquid properties which are expected to be governed by nonuniversal critical exponents.
The Kondo problem, which describes the interaction of a spin sss magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in 1/s1/s1/s with the renormalization group. We study both the case of an impurity interacting with a single channel K=1K=1K=1 of fermions in the s→∞s \rightarrow \inftys→∞ limit and the case with KKK channels in the double-scaling limit K→∞K \rightarrow \inftyK→∞, s→∞s \to \inftys→∞, K/sK/sK/s fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large sss and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime K>2sK > 2sK>2s we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.
A generalized Anderson model for a magnetic impurity in an interacting one-dimensional electron gas is studied via a mapping onto a classical Coulomb gas. For weak potential scattering, the local-moment parameter regime expands as repulsive bulk interactions become stronger, but the Kondo scale for the quenching of the impurity moment varies non-monotonically. There also exist two regimes dominated by backward potential scattering: one in which the impurity is non-magnetic, and another in which an unquenched local moment survives down to very low temperatures.