Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization

TL;DR

This paper investigates the critical behavior of Shannon and Renyi entropies in pure and random quantum Ising chains using real-space renormalization, revealing divergent and cusp singularities at quantum phase transitions.

Contribution

It applies self-dual Fernandez-Pacheco and Strong Disorder Renormalization methods to analyze entropy behavior at criticality in quantum Ising chains, highlighting differences between pure and random cases.

Findings

Logarithmic divergence of entropy derivative in pure case.

Cusp singularity in entropy derivative in random case.

Consistent results obtained via two renormalization approaches.

Abstract

The Shannon and the Renyi entropies of the ground state wavefunction in the pure and in the random quantum Ising chain are studied via the self-dual Fernandez-Pacheco real-space renormalization procedure. In particular, we analyze the critical behavior of the leading extensive term at the quantum phase transition : the derivative with respect to the control parameter is found to be logarithmically divergent in the pure case, and to display a cusp singularity in the random case. This cusp singularity for the random case is also derived via the Strong Disorder Renormalization approach.