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Spectral signatures of nonstabilizerness and criticality in infinite matrix product states

Andrew Hallam*, Ryan Smith*, and Zlatko Papić

  • *These authors contributed equally to this work.
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Phys. Rev. B 113, 245113 – Published 5 June, 2026

DOI: https://doi.org/10.1103/77wh-qv29

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 matrix product states “skeleton” of the cluster-Ising model, and we numerically probe its universal scaling along the Z2 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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      Phys. Rev. B 113, 245113– Published 5 June, 2026
      • Received 20 February 2026
      • Revised 20 April 2026
      • Accepted 28 April 2026
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      Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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