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 . In critical systems (Tomonaga-Luttinger liquids), we find that 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 chain. In a massive (crystal) phase, 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 critical point.
12 More- Received 8 June 2009
DOI:https://doi.org/10.1103/PhysRevB.80.184421
©2009 American Physical Society