  Electrons at the border of localization generate exotic states of matter
across all classes of strongly correlated electron materials and many other
quantum materials with emergent functionality. Heavy electron metals are a
model example, in which magnetic interactions arise from the opposing limits of
localized and itinerant electrons. This remarkable duality is intimately
related to the emergence of a plethora of novel quantum matter states such as
unconventional superconductivity, electronic-nematic states, hidden order and
most recently topological states of matter such as topological Kondo insulators
and Kondo semimetals and putative chiral superconductors. The outstanding
challenge is that the archetypal Kondo lattice model that captures the
underlying electronic dichotomy is notoriously difficult to solve for real
materials. Here we show, using the prototypical strongly-correlated
antiferromagnet CeIn$_3$, that a multi-orbital periodic Anderson model embedded
with input from ab initio bandstructure calculations can be reduced to a simple
Kondo-Heisenberg model, which captures the magnetic interactions
quantitatively. We validate this tractable Hamiltonian via high-resolution
neutron spectroscopy that reproduces accurately the magnetic soft modes in
CeIn$_3$, which are believed to mediate unconventional superconductivity. Our
study paves the way for a quantitative understanding of metallic quantum states
such as unconventional superconductivity.

Strongly Correlated Electrons