  The entanglement entropy of the ground state of a quantum lattice model with
local interactions usually satisfies an area law. However, in 1D systems some
violations may appear in inhomogeneous systems or in random systems. In our
inhomogeneous system, the inhomogeneity parameter, $h$, allows us to tune
different regimes where a volumetric violation of the area law appears. We
apply the strong disorder renormalization group to describe the maximally
entangled state of the system in a strong inhomogeneity regime. Moreover, in a
weak inhomogeneity regime, we use a continuum approximation to describe the
state as a thermo-field double in a conformal field theory with an effective
temperature which is proportional to the inhomogeneity parameter of the system.
The latter description also shows that the universal scaling features of this
model are captured by a massless Dirac fermion in a curved space-time with
constant negative curvature $R=-h^2$, providing another example of the relation
between quantum entanglement and space-time geometry. The results we discuss
here were already published before, but here we present a more didactic
exposure of basic concepts of the rainbow system for the students attending the
Latin American School of Physics Marcos Moshinsky 2017.
