Quantum XYZ and Clock Models Demonstrate Fidelity Zeros Within Ordered Regions Via Non-Hermitian Symmetry Breaking

Understanding the behaviour of complex quantum systems represents a major challenge in modern physics, and recent work by Tian-Yi Gu and Gaoyong Sun, from Nanjing University of Aeronautics and Astronautics, significantly advances this field. The researchers investigate how complex external forces influence fundamental quantum models, including the well-studied XY, XXZ, XYZ, and clock models, using a framework built upon Lee-Yang theory. Their findings reveal that these forces can disrupt the symmetry of these systems, causing oscillations in the ground state and leading to the emergence of ‘fidelity zeros’ which signal critical points. Importantly, this work extends the theoretical understanding of these phenomena and confirms analytical predictions through detailed analysis of the clock model, offering new insights into the behaviour of quantum systems near critical transitions. Fidelity Zeros and Quantum Phase Transitions This research significantly advances our understanding of complex quantum systems and how they undergo phase transitions, the points at which their fundamental properties change. Their work builds upon the Lee-Yang theory, a powerful tool originally developed for understanding classical phase transitions, and extends its reach to a broader range of quantum systems. The researchers focused on how complex external forces disrupt the symmetry of these quantum models, leading to oscillations in the ground state, the lowest energy configuration of the system. These oscillations manifest as ‘fidelity zeros’, specific points that signal the occurrence of critical transitions, where the system’s properties dramatically change.

Fidelity Zeros Reveal Quantum Phase Transitions Scientists have successfully extended the Lee-Yang theory to a broader range of quantum systems, providing a new framework for analyzing phase transitions. They discovered that these fields induce symmetry breaking and oscillations in the ground state, leading to the emergence of fidelity zeros which reliably signal phase transitions. The researchers mapped the distribution of these fidelity zeros by systematically varying the complex magnetic field and computing the ground state for each value. For the XY and XXZ models, the complex field breaks parity symmetry, causing oscillations between parity sectors and generating fidelity zeros within the ordered phase. In contrast, the Z3 clock model exhibits a different behaviour; the complex field splits the ground-state energy between neutral and charged sectors, but preserves degeneracy within the charged sectors. This work introduces the concepts of non-Hermitian symmetry breaking and fidelity zeros as key indicators of these transitions. Researchers subjected these models to complex external magnetic fields and discovered that these fields induce oscillations between parity sectors in the XY, XXZ, and XYZ models, directly leading to the emergence of fidelity zeros within the ordered phase. For the clock model, the complex field splits the ground-state energy between neutral and charged sectors while preserving degeneracy within the charged sectors, requiring a projection technique to clearly define symmetry breaking and detect fidelity zeros. Numerical computations reveal that the phase transition occurs at a specific field value, and as the system size increases, the real part of the field converges towards a critical point, confirming theoretical predictions. Detailed analysis of fidelity zeros reveals distinct distributions in both ordered and disordered phases, demonstrating the applicability of this fidelity-based approach to models with higher discrete symmetries, such as the Z3 clock model. Lee-Yang Theorem Extends to Quantum Systems This research successfully extends the Lee-Yang theory, traditionally used to understand phase transitions, to a broader range of quantum systems. They demonstrate that complex fields induce symmetry breaking and oscillations in the ground state, leading to the emergence of fidelity zeros which reliably signal phase transitions. The researchers found that complex fields split the ground-state energy between neutral and charged sectors while preserving degeneracy within the charged sectors, requiring a projection technique to clearly define symmetry breaking and detect fidelity zeros. Detailed analysis of fidelity zeros reveals distinct distributions in both ordered and disordered phases, demonstrating the applicability of this fidelity-based approach to models with higher discrete symmetries, such as the Z3 clock model. The authors acknowledge that their current work focuses on systems with discrete symmetries and suggest a promising direction for future research lies in extending the framework to encompass continuous symmetry-breaking cases. 👉 More information 🗞 Non-Hermitian symmetry breaking and Lee-Yang theory for quantum XYZ and clock models 🧠 ArXiv: https://arxiv.org/abs/2512.08687 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. Latest Posts by Rohail T.: Topological Spin-Up Triplet Excitonic Condensation, Exhibiting Nonzero Chern Numbers, Emerges in 2D Systems December 11, 2025 Fastpose-vit: Vision Transformer Achieves Real-Time 6DoF Spacecraft Pose Estimation from Single Images December 11, 2025 Privacy-enhanced Vision Transformers on the Edge Address Data Vulnerabilities with Distributed Framework December 11, 2025