Spectral signatures of nonstabilizerness and criticality in infinite matrix product states

• URL: http://arxiv.org/abs/2602.15116v1
• Date: Mon, 16 Feb 2026 19:00:04 GMT
• Title: Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Authors: Andrew Hallam, Ryan Smith, Zlatko Papić,
• Abstract summary: We show that nonstabilizerness captures signatures of criticality and local perturbations.<n>Results provide a new lens on the interplay between computational resources and emergent phenomena in quantum many-body systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Rényi 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 $χ=2$ 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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