Ryan Smith (School of Physics and Astronomy, University of Leeds) – Spectral signatures of nonstabilizerness and criticality in infinite matrix product states

Nonstabilizerness or quantum magic is a fundamental resource required for universal quantum computation, however it’s role in many-body quantum systems, especially near criticality, remain poorly understood. Here, we develop a spectral transfer-matrix framework for the stabilizer Renyi 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 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.