01420nas a2200157   4500000000100000000000100001008004100002100002100043700001900064700001400083245008400097856007200181490000800253520098700261022001401248       2019                            d1 aZakaria Mzaouali1 aSteve Campbell1 aMorad Baz00aDiscrete and generalized phase space techniques in critical quantum spin chains  uhttps://www.sciencedirect.com/science/article/pii/S03759601193077650 v3833 a<p>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.</p>
  a0375-9601