Entanglement entropy of aperiodic quantum spin chains

TL;DR

This paper investigates how aperiodic modulations in quantum spin chains affect entanglement entropy, revealing logarithmic growth with oscillations and variable effective central charge, including exact calculations in strong modulation regimes.

Contribution

It provides a detailed analysis of entanglement entropy in aperiodic quantum spin chains, introducing a renormalization group approach for strong modulations and characterizing the scaling behavior.

Findings

Entanglement entropy shows logarithmic growth with log-periodic oscillations.

The effective central charge c_eff can vary with coupling ratios and exceed homogeneous values.

In strong modulation limits, c_eff is exactly computed using renormalization group methods.

Abstract

We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulations, the entanglement entropy is found to be a logarithmic function of the block size with log-periodic oscillations. The effective central charge, c_eff, defined through the constant in front of the logarithm may depend on the ratio of couplings and can even exceed the corresponding value in the homogeneous system. In the strong modulation limit, the ground state is constructed by a renormalization group method and the limiting value of c_eff is exactly calculated. Keeping the ratio of the block size and the system size constant, the entanglement entropy exhibits a scaling property, however, the corresponding scaling function may be nonanalytic.