Single hole dynamics in the Kondo Necklace and Bilayer Heisenberg models on a square lattice

Abstract

We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J_perp. At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p = (π,π) and an effective mass at this p-point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p = (π,π) remains finite for all considered values of J_perp such that the strong coupling features of the dispersion relation are apparent down to weak coupling. In contrast, in the bilayer Heisenberg model, the effective mass diverges at a finite value of J_perp. This divergence of the effective mass is unrelated to the magnetic quantum phase transition and at weak coupling the dispersion relation maps onto that of a single hole doped in a planar antiferromagnet with band maximum at p = (π/2,π/2). We equally study the behavior of the quasiparticle residue in the vicinity of the magnetic quantum phase transition both for a mobile and static hole. In contrast to analytical approaches, our numerical results do not unambiguously support the fact that the quasiparticle residue of the static hole vanishes in the vicinity of the critical point. The above results are obtained with a generalized version of the loop algorithm to include single hole dynamics on lattice sizes up to 20 X 20.