  A quantum critical point (QCP) arises at a continuous transition between
competing phases at zero temperature. Collective excitations at magnetic QCPs
give rise to metallic properties that strongly deviate from the expectations of
Landau's Fermi liquid description, the standard theory of electron correlations
in metals. Central to this theory is the notion of quasiparticles, electronic
excitations which possess the quantum numbers of the bare electrons. Here we
report measurements of thermal and electrical transport across the
field-induced magnetic QCP in the heavy-fermion compound YbRh$_2$Si$_2$. We
show that the ratio of the thermal to electrical conductivities at the
zero-temperature limit obeys the Wiedemann-Franz (WF) law above the critical
field, $B_c$. This is also expected at $B < B_c$, where weak antiferromagnetic
order and a Fermi liquid phase form below 0.07 K ($B = 0$). However, at the
critical field the low-temperature electrical conductivity suggests a
non-Fermi-liquid ground state and exceeds the thermal conductivity by about
10%. This apparent violation of the WF law provides evidence for an
unconventional type of QCP at which the fundamental concept of Landau
quasiparticles breaks down. These results imply that Landau quasiparticles
break up, and that the origin of this disintegration is inelastic scattering
associated with electronic quantum critical fluctuations. Our finding brings
new insights into understanding deviations from Fermi-liquid behaviour
frequently observed in various classes of correlated materials.
