  For a class of $D=5$ holographic models we construct boomerang RG flow
solutions that start in the UV at an $AdS_5$ vacuum and end up at the same
vacuum in the IR. The RG flows are driven by deformations by relevant operators
that explicitly break translation invariance. For specific models, such that
they admit another $AdS_5$ solution, $AdS_5^c$, we show that for large enough
deformations the RG flows approach an intermediate scaling regime with
approximate conformal invariance governed by $AdS^c_5$. For these flows we
calculate the holographic entanglement entropy and the entropic $c$-function
for the RG flows. The latter is not monotonic, but it does encapsulate the
degrees of freedom in each scaling region. For a different set of models, we
find boomerang RG flows with intermediate scaling governed by an
$AdS_2\times\mathbb{R}^3$ solution which breaks translation invariance.
Furthermore, for large enough deformations these models have interesting and
novel thermal insulating ground states for which the entropy vanishes as the
temperature goes to zero, but not as a power-law. Remarkably, the thermal
diffusivity and the butterfly velocity for these new insulating ground states
are related via $D=Ev^2_B/(2\pi T)$, with $E(T)\to 0.5$ as $T\to 0$.
