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

Abstract

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.

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• Negativity Spectrum in the Random Singlet Phase
• Unusual area-law violation in random inhomogeneous systems
• Disorder-assisted distribution of entanglement in $XY$ spin chains
• Casimir forces on deformed fermionic chains
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Link representation of the entanglement entropies for all bipartitions
• Entanglement generation between distant parties via disordered spin chains
• Entanglement links and the quasiparticle picture
• Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length
• Entanglement in non-critical inhomogeneous quantum chains
• Depletion in fermionic chains with inhomogeneous hoppings
• Exotic correlation spread in free-fermionic states with initial patterns
• Engineering large end-to-end correlations in finite fermionic chains