Non-Hermitian symmetry breaking and Lee-Yang theory for quantum XYZ and clock models

Abstract: Lee-Yang theory offers a unifying framework for understanding classical phase transitions and dynamical quantum phase transitions through the analysis of partition functions and Loschmidt echoes. Recently, this framework is extended to characterize quantum phase transitions in arXiv:2509.20258 by introducing the concepts of non-Hermitian symmetry breaking and fidelity zeros. Here, we generalize the theory by studying a broad class of quantum models, including the XY model, the XXZ model, the XYZ model, and the $\mathbb{Z}_3$ clock model in one dimension, subject to complex external magnetic field. For the XY, XXZ and XYZ models, we find that the complex field breaks parity symmetry and induces oscillations of the ground state between the two parity sectors, giving rise to fidelity zeros within the ordered phases. For the $\mathbb{Z}_3$ clock model, the complex field splits the real part of the ground-state energy between the neutral sector ($q=0$) and the charged sectors ($q=1,2$), while preserving the degeneracy within the charged sector. Fidelity zeros arise only after projecting out one of the charged sectors, and the finite-size scaling of these zeros produces critical exponents fully consistent with analytical predictions.