Boomerang RG flows with intermediate conformal invariance

TL;DR

This paper constructs holographic boomerang RG flows in five-dimensional models, revealing intermediate conformal regimes and novel insulating ground states with unique thermal and chaotic properties.

Contribution

It introduces new boomerang RG flow solutions with intermediate conformal invariance and explores their entanglement and thermal characteristics.

Findings

Identification of RG flows with intermediate $AdS_5^c$ scaling regimes.

Discovery of insulating ground states with non-power-law entropy vanishing.

Relation between thermal diffusivity and butterfly velocity in insulating states.

Abstract

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 $T\to 0$.