  The discovery of novel entanglement patterns in quantum many-body systems is
a prominent research direction in contemporary physics. Here we provide the
example of a spin chain with random and inhomogeneous couplings that in the
ground state exhibits a very unusual area law violation. In the clean limit,
i.e., without disorder, the model is the rainbow chain and has volume law
entanglement. We show that, in the presence of disorder, the entanglement
entropy exhibits a power-law growth with the subsystem size, with an exponent
1/2. By employing the Strong Disorder Renormalization Group (SDRG) framework,
we show that this exponent is related to the survival probability of certain
random walks. The ground state of the model exhibits extended regions of
short-range singlets (that we term ``bubble'' regions) as well as rare long
range singlet (``rainbow'' regions). Crucially, while the probability of
extended rainbow regions decays exponentially with their size, that of the
bubble regions is power law. We provide strong numerical evidence for the
correctness of SDRG results by exploiting the free-fermion solution of the
model. Finally, we investigate the role of interactions by considering the
random inhomogeneous XXZ spin chain. Within the SDRG framework and in the
strong inhomogeneous limit, we show that the above area-law violation takes
place only at the free-fermion point of phase diagram. This point divides two
extended regions, which exhibit volume-law and area-law entanglement,
respectively.
