Fidelity zeros and Lee-Yang theory of quantum phase transitions
Phys. Rev. B 113, 014417 – Published 14 January, 2026
DOI: https://doi.org/10.1103/3x34-f53v
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 remain 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 investigate fidelity zeros analytically in one-dimensional and numerically in two-dimensional quantum Ising models under a complex magnetic field, showing excellent agreement with analytical theory and with quantum Monte Carlo and tensor-network simulations. Our results provide insights into the mechanism of Lee-Yang theory and open avenues for exploring unexplored landscapes of phase transitions in quantum many-body systems.
