  Average block entanglement in the 1D XX-model with uncorrelated random
couplings is known to grow as the logarithm of the block size, in similarity to
conformal systems. In this work we study random spin chains whose couplings
present long range correlations, generated as gaussian fields with a power-law
spectral function. Ground states are always planar valence bond states, and
their statistical ensembles are characterized in terms of their block entropy
and their bond-length distribution, which follow power-laws. We conjecture the
existence of a critical value for the spectral exponent, below which the system
behavior is identical to the case of uncorrelated couplings. Above that
critical value, the entanglement entropy violates the area law and grows as a
power law of the block size, with an exponent which increases from zero to one.
Similar planar bond structures are also found in statistical models of RNA
folding and kinetic roughening, and we trace an analogy between them and
quantum valence bond states. Using an inverse renormalization procedure we
determine the optimal spin-chain couplings which give rise to a given planar
bond structure, and study the statistical properties of the couplings whose
bond structures mimic those found in RNA folding.
