# Renormalization group study of the Kondo problem at a junction of several Luttinger wires

Ravi Chandra, V and Rao, Sumathi and Sen, Diptiman (2007) Renormalization group study of the Kondo problem at a junction of several Luttinger wires. In: Physical Review-B, 75 (4). 045435:1-14.

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## Abstract

We study a system consisting of a junction of N wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons near the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group RG equations for the Kondo couplings of the spin to the electrons on different wires. We analyze the RG flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix, such as the decoupled S-matrix and the Griffiths connected S-matrix. We find that the Kondo couplings flow either towards a ferromagnetic FM fixed point or towards large and antiferromagnetic AFM values in one of two ways. For the Griffiths S-matrix, one of the strong coupling flows is towards a FM fixed point with decoupled wires; this is seen by a perturbative analysis. Thus if we start with a system of connected wires with an AFM coupling to the spin impurity, the flow at large distances is towards a system of disconnected wires at the FM fixed point. For the decoupled S-matrix, the flow is either to a FM fixed point or to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. Strong interactions between the electrons with $K_\rho< N/(N+2)$ can stabilize a multichannel fixed point in which the coupling between different channels goes to zero. We also study the temperature dependence of the conductance at the decoupled and Griffiths S-matrices.

Item Type: Journal Article Copyright of this article belongs to the American Physical Society. Division of Physical & Mathematical Sciences > Centre for High Energy Physics 28 Mar 2007 19 Sep 2010 04:36 http://eprints.iisc.ernet.in/id/eprint/10392