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arXiv · 2406.19457

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

A. G. Catalano·J. Odavić·G. Torre·A. Hamma·F. Franchini·S. M. Giampaolo
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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.

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A. G. Catalano, J. Odavić, G. Torre, A. Hamma, F. Franchini, S. M. Giampaolo. 2024-06-27. Magic phase transition and non-local complexity in generalized $W$ State. https://doi.org/10.21468/scipostphyscore.8.4.078

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