  Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van
Hove singularity of the electronic spectrum crosses the Fermi energy, is
expected to cause a change in the temperature dependence of the electrical
resistivity from its Fermi liquid behavior $\rho\sim T^{2}$ to $\rho\sim
T^{2}{\rm log}\left(1/T\right)$, a behavior consistent with experiments by
Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation
originates from the same multi-band scattering processes with large momentum
transfer that were recently shown to account for the linear in $T$ resistivity
of the strange metal Sr$_{3}$Ru$_{2}$O$_{7}$. In contrast, the thermal
resistivity $\rho_{Q}\equiv T/\kappa$, where $\kappa$ is the thermal
conductivity, is governed by qualitatively distinct processes that involve a
broad continuum of compressive modes, i.e. long wavelength density excitations
in Van Hove systems. While these compressive modes do not affect the charge
current, they couple to thermal transport and yield $\rho_{Q}\propto T^{3/2}$.
As a result, we predict that the Wiedemann-Franz law in strained
Sr$_{2}$RuO$_{4}$ should be violated with a Lorenz ratio $L\propto T^{1/2}{\rm
log}\left(1/T\right)$. We expect this effect to be observable in the
temperature and strain regime where the anomalous charge transport was
established.
