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

Jean Marie Stéphan, Shunsuke Furukawa, Grégoire Misguich, Vincent Pasquier

Research output: Contribution to journalArticle

104 Citations (Scopus)

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.

Original languageEnglish
Article number184421
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume80
Issue number18
DOIs
Publication statusPublished - 2009 Nov 20
Externally publishedYes

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Wave functions
Entropy
wave functions
entropy
Dimers
Ground state
dimers
Bosons
ground state
Probability distributions
critical point
Demonstrations
bosons
Gases
Crystals
radii
Liquids
liquids
gases
crystals

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Shannon and entanglement entropies of one- and two-dimensional critical wave functions. / Stéphan, Jean Marie; Furukawa, Shunsuke; Misguich, Grégoire; Pasquier, Vincent.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 80, No. 18, 184421, 20.11.2009.

Research output: Contribution to journalArticle

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