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arXiv · 2602.15116

Spectral signatures of nonstabilizerness and criticality in infinite matrix product states

Andrew Hallam·Ryan Smith·Zlatko Papić
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Abstract

While nonstabilizerness (''magic'') is a key resource for universal quantum computation, its behavior in many-body quantum systems, especially near criticality, remains poorly understood. We develop a spectral transfer-matrix framework for the stabilizer R\'enyi entropy (SRE) in infinite matrix product states, showing that its spectrum contains universal subleading information. In particular, we identify an SRE correlation length -- distinct from the standard correlation length -- which diverges at continuous phase transitions and governs the spatial response of the SRE to local perturbations. We derive exact SRE expressions for the bond dimension $\chi=2$ MPS ''skeleton'' of the cluster-Ising model, and we numerically probe its universal scaling along the $\mathbb{Z}_2$ critical lines in the phase diagram. These results demonstrate that nonstabilizerness captures signatures of criticality and local perturbations, providing a new lens on the interplay between computational resources and emergent phenomena in quantum many-body systems.

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Andrew Hallam, Ryan Smith, Zlatko Papić. 2026-02-16. Spectral signatures of nonstabilizerness and criticality in infinite matrix product states. https://doi.org/10.1103/77wh-qv29

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