Dr Salvatore Marco Giampaolo

Magic phase transition and non-local complexity in generalized W State

In the framework of topologically frustrated quantum systems, we employ the Stabilizer Rényi Entropy (SRE) to characterize a quantum phase transition that has so far eluded any standard description and can thus now be explained in terms of the interplay between its non-stabilizer properties and entanglement. This transition separates a region with a unique ground state from one with a degenerate ground state manifold spanned by states with opposite non-vanishing momenta. We show that SRE has a jump at the crossing points, while the entanglement entropy remains continuous. Moreover, by leveraging on a Clifford circuit mapping, we connect the observed jump in SRE to that occurring between standard and generalized W-states with finite momenta. This mapping allows us to quantify the SRE discontinuity analytically.