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Shannon and entanglement entropies of one- and two-dimensional critical wave functions

Jean-Marie Stéphan, Shunsuke Furukawa, Grégoire Misguich, and Vincent Pasquier
Phys. Rev. B 80, 184421 – Published 20 November 2009

Abstract

We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point.

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  • Received 8 June 2009

DOI:https://doi.org/10.1103/PhysRevB.80.184421

©2009 American Physical Society

Authors & Affiliations

Jean-Marie Stéphan1, Shunsuke Furukawa2, Grégoire Misguich1, and Vincent Pasquier1

  • 1Institut de Physique Théorique, CEA, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette, France
  • 2Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

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Issue

Vol. 80, Iss. 18 — 1 November 2009

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