Fidelity zeros and Lee-Yang theory of quantum phase transitions

• URL: http://arxiv.org/abs/2509.20258v1
• Date: Wed, 24 Sep 2025 15:45:10 GMT
• Title: Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Authors: Tian-Yi Gu, Gaoyong Sun,
• Abstract summary: We develop a unified framework for understanding quantum phase transitions from fidelity zeros induced by symmetry breaking.<n> fidelity zeros obey the Lee-Yang theorem and give rise to fidelity edges near critical points.<n>We analytically and numerically investigate fidelity zeros in one- and two-dimensional ferromagnetic Ising models under a complex magnetic field.
• Score: 2.9649783577150832
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Lee-Yang theory is central to the analysis of thermal phase transitions. However, the underlying mechanism of the theory and the nature of Lee-Yang zeros in quantum many-body systems remains elusive. Here, we develop a unified framework for understanding quantum phase transitions from fidelity zeros induced by symmetry breaking. These zeros, arising from transitions between symmetry sectors, obey the Lee-Yang theorem and give rise to fidelity edges near critical points. Quantum criticality is further characterized through the finite-size scaling of fidelity zeros. As concrete examples, we analytically and numerically investigate fidelity zeros in one- and two-dimensional ferromagnetic Ising models under a complex magnetic field. Our results provide new insights into the mechanism of Lee-Yang theory and open avenues for exploring unexplored landscapes of phase transitions in quantum many-body systems.

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