Fidelity zeros and Lee-Yang theory of quantum phase transitions

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.

6 pages, 5 figures

References in corpus (18)

• Topological Origin of Non-Hermitian Skin Effects
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Topological Non-Hermitian skin effect
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Observation of Lee-Yang zeros
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Experimental observation of the Yang-Lee quantum criticality in open systems
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Indication of critical scaling in time during the relaxation of an open quantum system
• Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Detecting Many-Body Scars from Fisher Zeros
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks