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For a class of $D=5$ holographic models we construct boomerang RG flowsolutions that start in the UV at an $AdS_5$ vacuum and end up at the samevacuum in the IR. The RG flows are driven by deformations by relevant operatorsthat explicitly break translation invariance. For specific models, such thatthey admit another $AdS_5$ solution, $AdS_5^c$, we show that for large enoughdeformations the RG flows approach an intermediate scaling regime withapproximate conformal invariance governed by $AdS^c_5$. For these flows wecalculate the holographic entanglement entropy and the entropic $c$-functionfor the RG flows. The latter is not monotonic, but it does encapsulate thedegrees of freedom in each scaling region. For a different set of models, wefind 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 andnovel thermal insulating ground states for which the entropy vanishes as thetemperature goes to zero, but not as a power-law. Remarkably, the thermaldiffusivity and the butterfly velocity for these new insulating ground statesare related via $D=Ev^2_B/(2\pi T)$, with $E(T)\to 0.5$ as $T\to 0$.

Boomerang RG flows with intermediate conformal invariance