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

TL;DR

This paper uses Stabilizer Renyi Entropy to identify a quantum phase transition characterized by a jump in non-stabilizer properties, linking it to generalized W-states and entanglement features.

Contribution

It introduces SRE as a tool to characterize a novel quantum phase transition and connects it to generalized W-states through a Clifford circuit mapping.

Findings

SRE exhibits a jump at the phase transition points.

Entanglement entropy remains continuous across the transition.

The SRE discontinuity is analytically quantifiable via a Clifford circuit mapping.

Abstract

We employ the Stabilizer Renyi 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. The transition under consideration separates a region with a unique ground state from one with a degenerate ground state manifold spanned by states with finite and opposite (intensive) 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.