Renormalization-group study of a magnetic impurity in a Luttinger liquid

– A generalized Anderson model for a magnetic impurity in an interacting onedimensional 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 nonmonotonically. 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. The notion of a “Luttinger liquid” has received much attention recently in connection with quantum wires, edge excitations in the fractional quantum Hall effect, and the normal state of high-Tc superconductors [1]. The observation that a single potential scatterer in an interacting one-dimensional (1D) electron system can cause the conductance to vanish [2] has generated particular interest. While the physics of a static impurity is largely understood, that of a dynamical impurity —a magnetic atom being a natural example— remains less clear. Even in a non-interacting host, a magnetic impurity can produce interesting many-body physics, in the form of the Kondo effect [3]. The combined treatment of bulk interactions and impurityinduced correlations, which may be necessary, for instance, to understand the heavy-fermion behaviour observed in Nd2−xCexCuO4 [4], is a considerable theoretical challenge. Most work on magnetic impurities in 1D systems [5] has focused on the Kondo model, presupposing the existence of a local moment. Repulsive bulk interactions have been found to make possible a Kondo effect for ferromagnetic (as well as antiferromagnetic) exchange couplings J , and to drive the form of the Kondo temperature TK (below which the exchange renormalizes to strong coupling) from an exponential in J to a power law. Analysis of an Anderson impurity in a restricted Luttinger model suggests that interactions expand the local-moment regime [6]. Certain parameter regimes of the full Anderson model have been () Present address: Department of Physics, Ohio State University, Columbus, Ohio 43210, USA. c © Les Editions de Physique 646 EUROPHYSICS LETTERS claimed to renormalize onto an equivalent impurity problem in a Fermi liquid [7], a result that is shown below to be an artefact of neglecting important couplings in the problem. Here we study a generalized Anderson model, which includes direct and exchange interactions between localized and delocalized electrons in addition to hybridization between the impurity and the Luttinger liquid. We investigate the competition between 1) mixed valence; 2) local-moment formation (and a subsequent Kondo effect); and 3) correlated behaviours arising from strong backward potential scattering [2]. The impurity problem is mapped onto a classical Coulomb gas, which is analyzed using perturbative renormalization-group (RG) methods. We find that repulsive bulk interactions tend to stabilize local-moment formation by suppressing charge transfer between the impurity and the host. With increasing interactions, the Kondo temperature first rises, but then falls due to the reduced hybridization. In addition to a magnetic phase dominated by spin exchange and a non-magnetic phase driven by backward potential scattering, there exists a novel regime which exhibits a Curie susceptibility down to low temperatures, but displays the anomalous transport properties of a static impurity. We begin with the Hamiltonian H = HLutt +Himp +Hhybrid +HKondo +Hdensity. Here,