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arXiv:2407.20106 · Physical review. B./Physical review. B

Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems

Ming-Chu Lu, Shun-Hui Shi, Gaoyong Sun

Published Feb 21, 2025• 9 citations
arXivHTMLPDF

Abstract

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 $\mathcal{PT}$-symmetric regime but exhibit nonunitary dynamics in the $\mathcal{PT}$-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.

DOI
10.1103/physrevb.111.054309

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•Jul 12, 2026•0 citations
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\mathcal{PT}PT-symmetric regime but exhibit nonunitary dynamics in the PT\mathcal{PT}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.
We present a comprehensive theoretical framework for quantum criticality in the non-Hermitian detuned PXP model, and establish the complete phase diagram, which had remained elusive in previous studies. Starting from a numerically identified phase transition point, we construct an exact second-order phase transition boundary through a similarity transformation in the real-energy regime. By introducing the biorthogonal entanglement entropy and biorthogonal Loschmidt echo, we demonstrate from both equilibrium and nonequilibrium perspectives that this transition belongs to the Ising universality class. Using the correlation function, we further distinguish between confined and deconfined phases within the PT\mathcal{PT}PT-symmetric region. In the complex-energy regime, we identify both a full PT\mathcal{PT}PT transition and a first-excited-state PT\mathcal{PT}PT transition, respectively. Moreover, we identify the location of the Yang-Lee edge singularity (YLES) using both the associated-biorthogonal and self-normal Loschmidt echoes, and extract the corresponding critical exponent, which agrees with the predictions of nonunitary conformal field theory. Finally, we propose an experimental scheme to observe the YLES in Rydberg atomic arrays, which offers a promising route to exploring non-Hermitian critical phenomena and singularities in future experimental settings.
The Yang-Lee edge singularity is a quintessential nonunitary critical phenomenon characterized by anomalous scaling. However, an imaginary magnetic field involved in this phenomenon makes its physical implementation nontrivial. By embedding the original classical system which exhibits the Yang-Lee edge singularity in a quantum system with an ancilla qubit and by invoking the quantum-classical correspondence, we demonstrate a physical realization of the nonunitary quantum criticality in an open quantum system, where the nonunitary criticality is identified with the singularity at an exceptional point caused by postselection of quantum measurement.
Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of nonunitary phase transitions in nonequilibrium settings. In particular, scaling analyses based on our nonunitary time evolution circuit with matrix product states accurately recover the exponents uniquely associated with the corresponding nonunitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards a universal platform for simulating non-Hermitian many-body dynamical phenomena.
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.
Abstract We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.
Non-Hermitian criticality is often treated as a single phenomenon, yet two distinct objects travel under that name. An exceptional point is a finite-N spectral object—the coalescence of eigenvectors of a single operator; a Lee–Yang edge is a thermodynamic-limit c-number object—the accumulation of partition-function zeros. We show that which of these an imaginary coupling produces is set by the direction the coupling occupies. When the coupling multiplies a conserved charge, [Q, H] = 0, the deformation H − iµQ is normal for every complex µ: its spectrum is entire, its eigenvectors are µ-independent, and no exceptional point exists at any coupling strength or volume, while Lee–Yang zeros persist and can carry an edge. When the coupling lies on a symmetry-invariant but non-conserved direction, exceptional points appear, but the associated universality is the analytic continuation of the Hermitian thermal transition, not the Yang–Lee edge. Only on the order-parameter (symmetry-odd) direction do the two coincide, at the M(2, 5) edge. The direction of an imaginary coupling therefore sets how much genuine non-unitarity its spectrum acquires. We give the theorem, a three-arm criterion, exactly solvable and exact-diagonalization checks, and falsifiable kill conditions.