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Average block entanglement in the 1D XX-model with uncorrelated randomcouplings is known to grow as the logarithm of the block size, in similarity toconformal systems. In this work we study random spin chains whose couplingspresent long range correlations, generated as gaussian fields with a power-lawspectral function. Ground states are always planar valence bond states, andtheir statistical ensembles are characterized in terms of their block entropyand their bond-length distribution, which follow power-laws. We conjecture theexistence of a critical value for the spectral exponent, below which the systembehavior is identical to the case of uncorrelated couplings. Above thatcritical value, the entanglement entropy violates the area law and grows as apower 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 RNAfolding and kinetic roughening, and we trace an analogy between them andquantum valence bond states. Using an inverse renormalization procedure wedetermine the optimal spin-chain couplings which give rise to a given planarbond structure, and study the statistical properties of the couplings whosebond structures mimic those found in RNA folding.

Entanglement in correlated random spin chains, RNA folding and kinetic roughening