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arXiv · 0906.1153

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

Jean-Marie Stéphan·Shunsuke Furukawa·Grégoire Misguich·Vincent Pasquier
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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 S_0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S_0 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, S_0 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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Jean-Marie Stéphan, Shunsuke Furukawa, Grégoire Misguich, Vincent Pasquier. 2009-10-22. Shannon and entanglement entropies of one- and two-dimensional critical wave functions. https://doi.org/10.1103/physrevb.80.184421

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