Non-stabilizerness as a Diagnostic of Criticality and Exceptional Points in Non-Hermitian Spin Chains

TL;DR

This paper explores how non-stabilizerness, or magic, can serve as a diagnostic tool for identifying critical points and exceptional degeneracies in non-Hermitian spin chains, revealing model-specific signatures of phase transitions.

Contribution

It introduces the use of stabilizer Rényi entropies to detect criticality and exceptional points in non-Hermitian quantum systems, demonstrating their effectiveness through analytical and numerical methods.

Findings

Magic peaks at Hermitian-like critical lines in the Ising chain.

Magic reaches maximum at exceptional points in the XX chain.

Finite-size effects enhance the sensitivity of magic as a marker.

Abstract

We investigate non-stabilizerness, 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 along 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 non-stabilizerness 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 is 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.