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.

arXiv commentv2=final version (15 pages, 6 figures)

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Cited by in corpus (8)

• Quantum entanglement in condensed matter systems
• Strong Disorder RG approach - a short review of recent developments
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry
• 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