Entanglement between random and clean quantum spin chains

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 subsystem and a random subsystem, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a doublelogarithmic fashion S ∼ 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 ∼l^-k. For k < 1/2, the entropy scales as S(k) ln 2(1 6-2k)ln L, while for k 1/2, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strongdisorder RG arguments.