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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.15116 |
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| _version_ | 1866914334018371584 |
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| author | Hallam, Andrew Smith, Ryan Papić, Zlatko |
| author_facet | Hallam, Andrew Smith, Ryan Papić, Zlatko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral signatures of nonstabilizerness and criticality in infinite matrix product states Hallam, Andrew Smith, Ryan Papić, Zlatko Quantum Physics 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. |
| title | Spectral signatures of nonstabilizerness and criticality in infinite matrix product states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.15116 |