Entanglement entropy in aperiodic singlet phases

TL;DR

This paper investigates how aperiodic sequences in XXZ chains influence entanglement entropy, revealing a piecewise linear growth with a logarithmic envelope characterized by an effective central charge that can surpass that of homogeneous models.

Contribution

It introduces a detailed analysis of entanglement entropy in aperiodic XXZ chains, identifying sequences with maximal effective central charge and exploring effects of marginal aperiodic modulations.

Findings

Entanglement entropy exhibits piecewise linear growth with a logarithmic envelope.

The effective central charge depends on the aperiodic sequence and can exceed that of homogeneous models.

Numerical results show a continuous variation of the effective central charge with coupling ratios.

Abstract

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