Competition and unification of Kondo coherence and magnetic ordering

Abstract

The heavy fermion quantum critical point is one of the most puzzling problems in the field of highly correlated electrons. This is a quantum critical point separating a non-magnetic heavy fermi liquid metal from an antiferromagnetically ordered metal. The major problem facing us is the fact that, based on new experiments, these two phases seem to collapse simultaneously at the quantum critical point, giving rise to a drastic change in the fermi surface across the transition. In the quest for a toy model to envision this simultaneous collapse, we study the Kondo-Heisenberg model on the honeycomb lattice at half-filling. We study a fixed point controlling the quantum phase transition of a Kondo coherent phase to a critical phase called algebraic spin liquid. Studying such a fixed point has been proposed to be key to understanding the quantum critical point in heavy fermions. The relativistic structure of the lowenergy theory is the hallmark of our theory. The critical theory, however, can only be managed by extending the spin flavors well beyond the physical up and down, a technique known as the "large-N expansion". We later approach the physical case of SU(2) spins head-on and propose a novel idea to unify the distinct Kondo coherent phase and antiferromagnetic phase. We propose destroying the Kondo phase by proliferating Kondo vortices. We show that spin-triplets can be created by a Kondo vortex because of the zero modes it generates at the chemical potential. This gives us a nice picture that a magnetic transition can be driven by proliferating Kondo vortices. We also identify a class of these spin-triplets that transform like a Néel order. Due to the half-filled limitation of this model, however, this Kondo-vortexdriven antiferromagentic transition is in the O(3) universality class. We also prove that, starting from the pure Kondo lattice model, due to the charge-conjugation symmetry, antiferromagentic Heisenberg exchange will be generated, and the pure Kondo lattice model transforms to the Kondo-Heisenberg model we have studied. A major asset of the model we have studied is that it can be simulated using a signfree quantum Monte Carlo method, and our analytical results can all be probed in numerics. We present our preliminary numerical results for this model.