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

TL;DR

This paper investigates the Shannon entropy of ground-state wave functions in one-dimensional quantum models, revealing universal behaviors and connections to entanglement entropy, with analytical and numerical results across different phases and models.

Contribution

It provides a field-theoretical analysis linking Shannon entropy to entanglement entropy and explores universal constants in critical and massive phases of quantum models.

Findings

S_0 is a universal constant in critical systems related to the boson radius

In massive phases, S_0 correlates with ground-state degeneracy

Numerical results confirm analytical predictions in specific models

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.