Entanglement between random and clean quantum spin chains

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 $\mathcal{S}\sim \ln \ln (L)$, 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 $\mathcal{S}(\kappa )\simeq (1-2\kappa )\mathcal{S}(\kappa =0)$, 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.

12 pages, 7 figures, Invited contribution to the Festschrift of John Cardy's 70th birthday

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Cited by in corpus (4)

• Strong Disorder RG approach - a short review of recent developments
• Unusual area-law violation in random inhomogeneous systems
• Entanglement across extended random defects in the XX spin chain
• Population boundary across an environmental gradient: Effects of quenched disorder