Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
arXiv:2412.07800 · doi:10.1103/PhysRevA.111.042204
Abstract
In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former.
References in corpus (35)
- Making Sense of Non-Hermitian Hamiltonians
- Complex Extension of Quantum Mechanics
- The physics of exceptional points
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Dynamical quantum phase transitions: a review
- Direct observation of dynamical quantum phase transitions in an interacting many-body system
- Observation of a dynamical topological phase transition
- Dynamical Topological Order Parameters far from Equilibrium
- Dynamical quantum phase transitions: scaling and universality
- Simulating dynamic quantum phase transitions in photonic quantum walks
- Observation of Lee-Yang zeros
- Observation of critical phenomena in parity-time-symmetric quantum dynamics
- Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
- Probing Lee-Yang zeros and coherence sudden death
- Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
- Experimental Determination of Dynamical Lee-Yang Zeros
- Entanglement in non-unitary quantum critical spin chains
- Engineering tunable local loss in a synthetic lattice of momentum states
- Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry
- Density of Zeros on the Lee-Yang circle obtained from magnetization data of a two-dimensional Ising ferromagnet
- Universal location of the Yang-Lee edge singularity in O(N) theories
- Yang-Lee edge singularity triggered entanglement transition
- Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays
- Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model
- Determination of universal critical exponents using Lee-Yang theory
- Probing Yang-Lee Edge Singularity by Central Spin Decoherence
- 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
- Entanglement Dynamics in Anti--Symmetric Systems
- Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence
- Infinite cascades of phase transitions in the classical Ising chain
- Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
- Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
- Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice