THE QUANTUM INTELLIGENCER

Non-Stabilizerness as a Quantum Diagnostic for Criticality and Exceptional Points in PT-Symmetric Spin Chains In Plain English: This research looks at a special property of quantum systems called 'magic,' which measures how complex or hard to simulate a state is. Scientists studied two types of quantum chains to see how this magic changes when the system undergoes major shifts, like phase transitions or hits special points where energy levels merge. They found that in one chain, magic spikes during normal phase transitions but disappears at these special points, while in another chain, magic peaks exactly at those points. This shows that magic can act like a sensitive detector for different kinds of quantum behavior. Understanding this helps physicists better identify and classify exotic states of matter, especially in systems that lose energy or interact with their environment. Summary: This paper investigates the role of non-stabilizerness—also known as 'magic'—as a diagnostic tool for quantum criticality and exceptional points in non-Hermitian many-body systems, with a focus on parity-time (PT) symmetric spin chains. The authors study two models: the non-Hermitian transverse-field Ising model and the non-Hermitian XX model. Using non-Hermitian matrix product state methods, they compute stabilizer Rényi entropies to quantify magic in the ground states. In the Ising model, non-stabilizerness peaks along the Hermitian-like critical line but vanishes across exceptional points, indicating a loss of quantum complexity at spectral degeneracies. In contrast, in the XX model, magic reaches its maximum at the exceptional line where PT symmetry is broken, suggesting enhanced complexity at symmetry-breaking transitions. Finite-size scaling confirms that these effects intensify with system size, underscoring the robustness and sensitivity of magic as a probe. Analytically, the authors examine the momentum-space distribution of magic in the XX model and find it reaches a minimum near exceptional points. These results demonstrate that non-stabilizerness exhibits extremal behavior at critical and exceptional points, making it a powerful and model-dependent indicator of both quantum phase transitions and non-Hermitian spectral phenomena. The work positions magic as a valuable resource-theoretic measure for characterizing complexity, criticality, and symmetry breaking in non-Hermitian quantum matter. Key Points: - Non-stabilizerness (magic) serves as a sensitive diagnostic for quantum criticality and exceptional points in non-Hermitian systems. - The behavior of magic is model-dependent: it peaks at Hermitian-like critical lines in the Ising model but vanishes at exceptional points. - In the XX model, magic reaches a maximum at the exceptional line where PT symmetry is broken. - Finite-size scaling shows that magic's response to criticality becomes more pronounced in larger systems. - Analytical results for the XX model in momentum space show magic reaches a minimum near exceptional points. - Magic exhibits extremal values at both critical and exceptional points, highlighting its utility as a probe of quantum complexity. - The study uses stabilizer Rényi entropies and non-Hermitian matrix product state methods to quantify magic in ground states. Notable Quotes: - "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..." - "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." Data Points: - The paper does not provide specific numerical values or dates beyond the theoretical framework and qualitative behaviors (e.g., 'peaks,' 'vanishes,' 'reaches maximum'). However, it mentions the use of finite-size scaling to confirm that the observed effects become more pronounced with increasing system size, indicating numerical validation across multiple lattice sizes. The models studied are defined in the thermodynamic limit, and the analytical treatment applies to the XX model in momentum space. Controversial Claims: - The claim that non-stabilizerness vanishes at exceptional points in the Ising model while peaking at the same type of points in the XX model may challenge expectations of universality in critical behavior across different models. This model-dependent response could raise questions about the generalizability of magic as a universal order parameter for non-Hermitian transitions. Additionally, the suggestion that magic—a resource from quantum computation theory—can serve as a primary diagnostic for symmetry breaking and spectral degeneracies may represent a strong conceptual shift, implying that computational complexity measures are as fundamental as traditional thermodynamic or symmetry-based indicators in quantum phase transitions. Technical Terms: - non-stabilizerness, magic, stabilizer Rényi entropy, non-Hermitian systems, exceptional points, PT symmetry, quantum criticality, phase transitions, spin chains, transverse-field Ising model, XX model, matrix product states (MPS), non-Hermitian matrix product state methods, ground state, spectral degeneracy, quantum complexity, resource theory, momentum space, finite-size scaling —Ada H. Pemberley Dispatch from The Prepared E0