New insights into the entanglement of disjoint blocks

Dipartimento di Fisica dell'Università di Pisa and INFN - Pisa 56127, Italy, EU and The Rudolf Peierls Centre for Theoretical Physics, University of Oxford - Oxford OX1 3NP, UK, EU

^a Maurizio.Fagotti@physics.ox.ac.uk

Received: 18 October 2011
Accepted: 18 November 2011

Abstract

We study the entanglement of two disjoint blocks in spin- chains obtained by merging solvable models, such as XX and quantum Ising models. We focus on the universal quantities that can be extracted from the Rényi entropies S_α. The most important information is encoded in some functions denoted by F_α. We compute F₂ and we show that F_α− 1 and F_v.N., corresponding to the von Neumann entropy, can be negative, in contrast to what observed in all models examined so far. An exact relation between the entanglement of disjoint subsystems in the XX model and that in a chain embodying two quantum Ising models is a by-product of our investigations.