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

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.

v2=final version (15 pages, 6 figures)

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Cited by in corpus (3)

• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study