2026-10-28 · arXiv Quantum Physics
arXiv:2510.17248v2 Announce Type: replace
Abstract: We investigate nonstabilizerness, also known as ``magic,'' to understand criticality and exceptional points in non-Hermitian quantum many-body systems. Our focus is on parity-time ($\mathcal{PT}$)-symmetric spin chains, specifically the non-Hermitian transverse-field Ising and XX models. We calculate stabilizer R\'enyi entropies in their ground states using non-Hermitian matrix product state methods. Our findings show that magic exhibits unique and model-specific signs of phase transitions. In the Ising chain, it peaks near the regular Hermitian-like critical line but disappears across exceptional points. In contrast, in the XX chain, it reaches its maximum at the exceptional line where $\mathcal{PT}$ symmetry is broken. Finite-size scaling reveals that these effects become more pronounced with larger systems, highlighting nonstabilizerness as a sensitive marker for both quantum criticality and non-Hermitian spectral degeneracies. We also investigate magic in momentum space for the XX model analytically and find that it reaches a minimum around exceptional points. Our results indicate that magic takes extremal values at the exceptional points and serves as a valuable tool for examining complexity, criticality, and symmetry breaking in non-Hermitian quantum matter.
原文链接：https://arxiv.org/abs/2510.17248
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