Discrete and generalized phase space techniques in critical quantum spin chains

TitleDiscrete and generalized phase space techniques in critical quantum spin chains
Publication TypeJournal Article
Year of Publication2019
AuthorsMzaouali Z, Campbell S, Baz MEl
JournalPhysics Letters A
Volume383
ISSN0375-9601
KeywordsQuantum Correlations, Quantum Phase transitions, Quantum Spin Chains, Wigner function
Abstract

We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-12 systems. We develop a general formula relating the phase space techniques and the thermodynamical quantities of spin models, which we apply to single, bipartite and multi-partite systems governed by the XY and the XXZ models. Our approach allows us to introduce a novel way to represent, detect, and distinguish first-, second- and infinite-order quantum phase transitions. Furthermore, we show that the factorization phenomenon of the XY model is only directly detectable by quantities based on the square root of the bipartite reduced density matrix. We establish that phase space techniques provide a simple, experimentally promising tool in the study of many-body systems and we discuss their relation with measures of quantum correlations and quantum coherence.

URLhttps://www.sciencedirect.com/science/article/pii/S0375960119307765
DOI10.1016/j.physleta.2019.125932