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.
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Cécile Monthus. Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2015, 2015 (04), pp.P04007. ⟨10.1088/1742-5468/2015/04/P04007⟩. ⟨cea-01322501⟩

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