Topological Kondo effect in star junctions of Ising magnetic chains: exact solution

Abstract

In this paper, I present a conjecture for the Bethe ansatz equations for the model describing a star junction of M quantum critical Ising chains. For $M>3$ such a model exhibits the so-called topological Kondo effect (Beri and Cooper 2012 Phys. Rev. Lett. 109 156803) related to the existence of Majorana zero energy modes at the junction. These modes are of a topological nature; they non-locally encode an SO(M) ‘spin’ which is screened by the collective excitations of the chains. For certain values of M , the model is equivalent to the Kondo models with a known exact solution. These cases are used to check the validity of the conjecture. It is demonstrated that the model behaves differently for M even and odd; in the former case the model has a Fermi liquid and the latter case corresponds to a non-Fermi liquid infrared fixed point.

Keywords

• Majorana fermions
• Kondo effect
• exact solution
• 74.81.Fa
• 74.90.+n