Entanglement entropy in aperiodic singlet phases

Abstract

We study the average entanglement entropy of blocks of contiguous spins in aperiodicXXZ chains which possess an aperiodic singlet phase at least in a certain limit of thecoupling ratios. In this phase, where the ground state constructed by a real spacerenormalization group method consists (asymptotically) of independent singlet pairs, theaverage entanglement entropy is found to be a piecewise linear function of theblock size. The enveloping curve of this function is growing logarithmically withthe block size, with an effective central charge in front of the logarithm whichis characteristic for the underlying aperiodic sequence. The aperiodic sequenceproducing the largest effective central charge is identified, and the latter isfound to exceed the central charge of the corresponding homogeneous model.For marginal aperiodic modulations, numerical investigations performed for theXX model show a logarithmic dependence, as well, with an effective central charge varyingcontinuously with the coupling ratio.