Siddhartha Patra   Abhirup Mukherjee   Anirban Mukherjee   N. S. Vidhyadhiraja   A. Taraphder   Siddhartha Lal  

The multichannel Kondo model consists of $K$ conduction channels $\vec S_i$ interacting with an impurity spin of strength $S_d$ (the Kondo model corresponds to $K=1,S_d=1/2$ ). It is well-known that the overscreened case $(K > 2S_d)$ corresponds to a degenerate ground state, incomplete quenching of the local moment and non-Fermi liquid excitations characterised by anomalous zero temperature divergences in thermodynamic quantities like the specific heat and susceptibility. Nevertheless, there was no ab initio derivation of the non-Fermi liquid Hamiltonian that describes these excitations. Neither had the precise role of quantum frustration in this problem and the effect of degeneracy on the low-energy physics been made clear. The frustration arises in this problem because the impurity is unable to form a singlet with a single conduction channel.

We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids. The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature, signaling its critical nature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them.

A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local non-Fermi liquids arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signaling the underlying orthogonality catastrophe associated with the degenerate ground state manifold.

We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling. Feel free to check out the ar$\chi$iv preprint.