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

TL;DR

This paper investigates how long-range correlations in random spin chains affect entanglement entropy, revealing a critical spectral exponent and drawing parallels with RNA folding and kinetic roughening phenomena.

Contribution

It introduces a model of correlated random spin chains with power-law spectral functions and analyzes their entanglement properties and bond structures, establishing connections with biological and physical systems.

Findings

Entanglement entropy transitions from logarithmic to power-law growth at a critical spectral exponent.

Planar valence bond states are characterized by power-law distributions of bond lengths.

Optimal couplings can be engineered to replicate bond structures seen in RNA folding.

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.