# Entanglement between random and clean quantum spin chains

## TL;DR

This paper investigates entanglement entropy in composite quantum spin chains combining clean and random parts, revealing a double-logarithmic growth and effects of extended defects, explained via strong-disorder RG methods.

## Contribution

It introduces the analysis of entanglement in mixed clean and random critical spin chains, including the impact of extended defects with decaying disorder.

## Key findings

- Entanglement entropy grows as ln ln L in clean-random chains.
- Extended defects with decay exponent κ affect entropy scaling.
- For κ ≥ 1/2, the double-logarithmic scaling is recovered.

## Abstract

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$, where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$. For $\kappa<1/2$, the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$, while for $\kappa \ge 1/2$, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.