Zooming in on heavy fermions in Kondo lattice models

Abstract

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as $e^{-W/J_k}$ with $W$ the bandwidth and $J_k$ the Kondo coupling, the residue of the composite fermion tracks $J_k$. This result holds down to $J_k/W = 0.05$, and confirms the point of view that magnetic ordering, present below $J_k/W = 0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for SU($N$) generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large $J_k$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.