Thermodynamics of the Topological Kondo Model

TL;DR

This paper employs the thermodynamic Bethe ansatz to analyze the topological Kondo model, revealing the role of Majorana bound states, fermion parity, and non-Fermi-liquid behavior at finite temperatures.

Contribution

It provides an exact thermodynamic analysis of the topological Kondo model, including free energy, ground state energy, and impurity entropy for arbitrary wire configurations.

Findings

Impurity entropy highlights fermion parity importance.

Low-temperature specific heat indicates non-Fermi-liquid behavior.

Ground state energy depends on the number of wires and couplings.

Abstract

Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.