Pure and random quantum Ising chain: Shannon and Rényi entropies of the ground state via real space renormalization. (22nd April 2015)

• Record Type: Journal Article
• Authors: Monthus, Cécile
• Is Part Of: Journal of statistical mechanics. (2015:Apr.)
• Publication Date: 2015-04-22
• Subjects: 2 -- 3; 2/090 -- 2/360 -- 3/170 -- 3/180; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/04/P04007
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The Shannon and the Rényi 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.