Critical points and non-Fermi liquids in the underscreened pseudogap Kondo model

TL;DR

This paper analyzes the universal low-energy behavior of the underscreened spin-1 Kondo model with a power-law bath, revealing non-Fermi liquid phases and critical points through renormalization group methods and numerical comparisons.

Contribution

It develops a universal low-energy theory for the underscreened pseudogap Kondo model, including critical exponents and fixed points, extending understanding of non-Fermi liquids in this context.

Findings

Identification of stable non-Fermi liquid fixed point at strong coupling

Universal field theory for particle-hole asymmetric critical point

Agreement between RG analysis and numerical data

Abstract

Numerical Renormalization Group simulations have shown that the underscreened spin-1 Kondo impurity model with power-law bath density of states (DOS) $\rho(\w) \propto |\w|^r$ possesses various intermediate-coupling fixed points, including a stable non-Fermi liquid phase. In this paper we discuss the corresponding universal low-energy theories, obtain thermodynamic quantities and critical exponents by renormalization group analysis together with suitable $\epsilon$-expansions, and compare our results with numerical data. Whereas the particle-hole symmetric critical point can be controlled at weak coupling using a simple generalization of the spin-1/2 model, we show that the stable non-Fermi liquid fixed point must be accessed near strong coupling via a mapping onto an effective ferromagnetic $S_\mr{eff}=1/2$ model with singular bath DOS with exponent $r_\mr{eff}=-r<0$. In addition, we consider the particle-hole asymmetric critical fixed point, for which we propose a universal field theory involving the crossing between doublet and triplet levels.