The Yang-Lee edge singularity is an intriguing critical phenomenon characterized by nonunitary field theory. However, its experimental realization for interacting many-body systems remains elusive. We show that Yang-Lee edge singularities, regarded as many-body exceptional points, can be observed using both the self-normal and the associated-biorthogonal Loschmidt echoes, leveraging the advantages of nonunitary dynamics in non-Hermitian systems. The Loschmidt echoes are demonstrated to display unitary dynamics in the
PT-symmetric regime but exhibit nonunitary dynamics in the
PT-symmetry-broken regime, leading to a sharp change near an exceptional point. We hereby identify exceptional points in both the non-Hermitian transverse-field Ising model and the Yang-Lee model, and determine the critical exponent that is consistent with nonunitary conformal field theory. This paper provides a direct observation of Yang-Lee edge singularities in non-Hermitian many-body systems arising from nonunitary dynamics.
Lee–Yang theory clearly demonstrates where the phase transition of many-body systems occurs and the asymptotic behavior near the phase transition using the partition function under complex parameters. The complex parameters make the direct investigation of Lee–Yang theory in practical systems challenging. Here we construct a non-Hermitian quantum system that can correspond to the one-dimensional Ising model with imaginary parameters through the equality of partition functions. By adjusting the non-Hermitian parameter, we successfully obtain the partition function under different imaginary magnetic fields and observe the Lee–Yang zeros. We also observe the critical behavior of free energy in vicinity of Lee–Yang zero that is consistent with theoretical prediction. Our work provides a protocol to study Lee–Yang zeros of the one-dimensional Ising model using a single-qubit non-Hermitian system.
We show that the
d+0-dimensional Yang-Lee theory describing classical Ising spins in an imaginary magnetic field can be realized, without post-selection, within a
(d−1)+1 open quantum system whose dynamics consist of local unitaries and engineered dissipation. Competition between the coherent unitary and dissipative dynamics drives a transition wherein the time-dependence of a particular class of linear observables changes from damped oscillatory "underdamped" to purely exponential "overdamped" decay. Our construction relies on an extensive number of weak-symmetries of the Lindbladian fixed by the choice of observable but is otherwise exact. Consequently, we show that the dynamics are described by the non-Hermitian generator of the Yang-Lee transfer matrix, leading to an effective Yang-Lee theory defined on the spacetime history of the open system. By locally modifying the dynamics, we directly measure spin correlation functions of the Yang-Lee theory as well as a related "Loschmidt Echo" correlator which we detail. We explicitly show that the required dissipation channels can be obtained through local
2-qubit gates and discuss potential realization on near-term quantum simulator devices. Finally, we generalize our construction to embed arbitrary non-Hermitian Hamiltonians within an open quantum system under Lindbladian time-evolution without post-selection, drawing connections between unconditional open quantum dynamics, exceptional point physics, and non-unitary statistical mechanics.
Abstract Recently, scaling behavior in Yang-Lee edge singularities (YLES) has attracted sustained attention. However, the scaling mechanism in the overlapping critical region between classical and quantum YLES remains unclear. In this work, we apply established renormalization group (RG) crossover theory to non-Hermitian YLES system. We demonstrate that, in the overlapping critical region between classical and quantum YLES, the scaling behavior can be described by a hybrid scaling mechanism, which asserts that scaling functions from both critical regimes apply simultaneously and satisfy a constraint relation. The transverse Ising chain in an imaginary longitudinal field is employed as a model to test this hybrid scaling mechanism. This model exhibits zero-dimensional (0D) and one-dimensional (1D) quantum YLES phase transitions at zero temperature, as well as 0D and 1D classical YLES phase transitions at finite temperature. We systematically investigate the scaling functions in the critical regions of 0D and 1D quantum YLES and those of 0D and 1D classical YLES. Furthermore, the hybrid scaling mechanisms in the overlapping critical regions, particularly between classical and quantum YLES, are thoroughly examined. Our results provide a concrete realization of quantum-to-classical crossover in a non-Hermitian YLES system and establish a hybrid scaling framework that captures critical behavior in overlapping regions between classical and quantum phase transitions. This framework enables the extraction of quantum critical information from finite-temperature classical measurements, thereby bridging the two paradigms and offering a pathway to probe quantum criticality experimentally.
We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).
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 of quantum Ising models by introducing the concepts of non-Hermitian parity-symmetry breaking and fidelity zeros. Here, we generalize the theory by studying a broad class of quantum models, including the XY, the XXZ, the XYZ, and the
Zp clock models in one dimension, subject to a complex 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
Z3 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. For the
Z4 and
Z5 clock models, the ground states are instead projected to oscillate between the neutral sector (
q=0) and the charged sectors
q=2 and
q=1, respectively, giving rise to fidelity zeros. Finite-size scaling of these zeros yields critical exponents in full agreement with analytical predictions, demonstrating that this approach is applicable not only to the Ising model with
Z2 symmetry, but also to more general Heisenberg-type models and systems with higher discrete symmetries.