Quantum phase transitions and thermodynamics of the power-law Kondo model

TL;DR

This paper investigates the quantum phase transitions and thermodynamics of a Kondo impurity model with a diverging power-law density of states, combining analytical fixed point analysis with numerical renormalization group methods.

Contribution

It provides a comprehensive analysis of the stable phases and quantum critical points of the power-law Kondo model with negative exponent, including new fermionic field theories for the critical fixed points.

Findings

Antiferromagnetic Kondo coupling causes strong screening and negative impurity entropy.

Ferromagnetic Kondo coupling can stabilize a fractional spin moment.

The study maps the phase diagram and characterizes quantum phase transitions.

Abstract

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.