Entanglement properties of correlated random spin chains and similarities with conformal invariant systems

TL;DR

This paper investigates the entanglement properties of correlated random XXZ spin chains, revealing that their entanglement entropy behaviors resemble those of conformally invariant systems despite not being conformally invariant, and extends conjectures about universal behavior.

Contribution

It demonstrates that correlated-disorder XXZ chains exhibit entanglement scaling similar to conformal systems, extending the understanding of universality in disordered quantum critical chains.

Findings

Correlated-disorder chains governed by finite-disorder fixed points.

Leading entanglement behavior matches conformal invariant systems.

Universal behavior extends to Shannon mutual information.

Abstract

We study the R\'enyi entanglement entropy and the Shannon mutual information for a class of spin-1/2 quantum critical XXZ chains with random coupling constants which are partially correlated. In the XX case, distinctly from the usual uncorrelated random case where the system is governed by an infinite-disorder fixed point, the correlated-disorder chain is governed by finite-disorder fixed points. Surprisingly, we verify that, although the system is not conformally invariant, the leading behavior of the R\'enyi entanglement entropies are similar to those of the clean (no randomness) conformally invariant system. In addition, we compute the Shannon mutual information among subsystems of our correlated-disorder quantum chain and verify the same leading behavior as the $n=2$ R\'enyi entanglement entropy. This result extends a recent conjecture concerning the same universal behavior of these quantities for conformally invariant quantum chains. For the generic spin-1/2 quantum critical XXZ case, the true asymptotic regime is identical to that in the uncorrelated disorder case. However, these finite-disorder fixed points govern the low-energy physics up to a very long crossover length scale and the same results as in the XX case apply. Our results are based on exact numerical calculations and on a numerical strong-disorder renormalization group.