Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions

Abstract

Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent α. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to N ∼ 18 spins, we find indications of a delocalization transition at αc ≈ 1 in the middle of the energy spectrum. With RSRG-X and ED, we show that for α > α * the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for α < α * EE displays an algebraic growth with the subsystem size l, S l ∼ l β , with 0 < β < 1. We find that α * ≈ 1 coincides with the delocalization transition αc in the middle of the many-body spectrum.An interpretation of these results based on the structure of the RG rules is proposed, which is due to rainbow proliferation for very long-range interactions α 1. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at α * < 1.

Entanglement entropy of XX spin $1/2$ chain with random partitioning

“…(with open boundary condition) where J n are distributed randomly by a distribution function (to be determined later). This model has been studied, regarding its entanglement properties before [27][28][29][30] . We want to obtain the entanglement properties of this model, specially we want to calculate EE.…”