Quantum critical point in the Kondo-Heisenberg model on the honeycomb lattice

TL;DR

This paper investigates a quantum phase transition in the Kondo-Heisenberg model on a honeycomb lattice, revealing a non-Fermi liquid critical point between a Kondo insulator and an algebraic spin liquid.

Contribution

It introduces a large-N renormalization group analysis of the KI to ASL transition, identifying a stable Lorentz-invariant fixed point without symmetry breaking.

Findings

Identifies a second order quantum phase transition controlled by a Lorentz-invariant fixed point.

Calculates critical exponent ν for the diverging correlation length.

Shows the quasi-particle weight vanishes, indicating non-Fermi liquid behavior.

Abstract

We study the Kondo--Heisenberg model on the honeycomb lattice at half-filling. Due to the vanishing of the density of states at the fermi level, the Kondo insulator disappears at a finite Kondo coupling even in the absence of the Heisenberg exchange. We adopt a large-N formulation of this model and use the renormalization group machinery to study systematically the second order phase transition of the Kondo insulator (KI) to the algebraic spin liquid (ASL). We note that neither phase breaks any physical symmetry, so that the transition is not described by the standard Ginzburg-Landau-Wilson critical point. We find a stable Lorentz-invariant fixed point that controls this second order phase transition. We calculate the exponent $\nu$ of the diverging length scale near the transition. The quasi-particle weight of the conduction electron vanishes at this KI--ASL fixed point, indicating non-Fermi liquid behavior. The algebraic decay exponent of the staggered spin correlation is calculated at the fixed point and in the ASL phase. We find a jump in this exponent at the transition point.