Multifractality in aperiodic quantum spin chains

TL;DR

This paper investigates the multifractal properties of the ground-state wavefunction in a quantum Ising chain with aperiodic perturbations, revealing how different wandering exponents affect multifractality.

Contribution

It introduces a real-space renormalization approach to analyze multifractality in aperiodic quantum spin chains, highlighting the impact of wandering exponents.

Findings

Multifractal quantities match the unperturbed chain for negative wandering exponent.

For zero wandering exponent, multifractal properties depend on the coupling ratio.

Positive wandering exponent leads to non-linear behavior in multifractal measures.

Abstract

Recently has been investigated that the ground-state wavefunction of the one dimensional quantum spin-1/2 chain models is multifractal in general with non-trivial fractal dimension. We are studying this phenomena for the quantum Ising chain with an aperiodic perturbation. By performing a block real-space renormalization approach, we obtain the ground-state wave function and we extract the generalized fractal dimension and the multifractal spectrum. For a spin chain with negative wandering exponent the multifractal quantities have the same behavior with the unperturbed chain while for a spin chain with a vanishing wandering exponent are dependent on the coupling ratio. Finally, for a spin chain with positive wandering exponent, the multifractal quantities present a different non-linear behavior.