Large-N analysis of the local quantum critical point and the spin-liquid phase

Abstract

We analytically study a Kondo lattice model with an additional nearest-neighbor antiferromagnetic interaction in the framework of large-$\mathcal{N}$ theory. We find that there is a local quantum critical point between two phases, a normal Fermi liquid and a spin liquid in which the spins are decoupled from the conduction electrons. The local spin susceptibility displays a power-law divergence throughout the spin liquid phase. We check the reliability of the large-$\mathcal{N}$ results by solving with a quantum Monte Carlo simulation, the $\mathcal{N}=2$ spin-liquid problem with no conduction electrons, and we find qualitative agreement. We show that the spin-liquid phase is unstable at low temperatures, suggestive of a first-order transition to an ordered phase.