Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2501.13654 · Physical review. B./Physical review. B

Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model

D. C. Liu, Murray T. Batchelor

Published Jun 23, 2025• 9 citations
arXivHTMLPDF

Abstract

In this work we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a new universality class with unusual critical exponent. We also emphasize the ability of the Loschmidt echo to characterize potential phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.

DOI
10.1103/b55l-7tbc

Related papers

Quantum critical properties of non-Hermitian XY models with magnetic field

Jia-Jia Luo, Volker Meden

The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.

quant-pharXiv:2606.07275•Jun 8, 2026•0 citations

Probing phase transitions in non-Hermitian systems with quantum entanglement

Lingfeng Zhang, Wing Chi Yu

We study the quantum entanglement and quantum phase transition of the non-Hermitian anisotropic spin-$\frac{1}{2}$ XY model and XXZ model with the staggered imaginary field by analytical methods and numerical exact diagonalization, respectively. Various entanglement measures, including concurrence, negativity, mutual information, and quantum coherence, and both biorthogonal and self-normal quantities are investigated. Both the biorthogonal and self-normal entanglement quantities, except the biorthogonal concurrence, are found to be capable of detecting the first-order and $\mathcal{PT}$ transitions in the XXZ model, as well as the Ising and $\mathcal{RT}$ transitions in the XY model. In addition, we introduce the unconstrained concurrence and demonstrate its effectiveness in detecting these transitions. On the other hand, the Berezinskii-Kosterlitz-Thouless (BKT) transition in the XXZ model is revealed through concurrence and negativity at small non-Hermiticity strengths. Notably, the critical points observed in the Hermitian limit evolve into exceptional points as the strength of the non-Hermiticity increases. Furthermore, we find that the first-order transition survives up to a higher non-Hermiticity strength compared to the BKT transition within the $\mathcal{PT}$-symmetric regime of the XXZ model.

arXiv:2509.25703•Physical review. B./Physical review. B•Sep 26, 2025•0 citations

Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model

Wen-Yi Zhang, Meng-Yun Mao, Qing-Min Hu +3 more

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 $\mathcal{PT}$-symmetric region. In the complex-energy regime, we identify both a full $\mathcal{PT}$ transition and a first-excited-state $\mathcal{PT}$ 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.

arXiv:2510.13581•Physical review. B./Physical review. B•Sep 25, 2025•6 citations

Survival of Hermitian Criticality in the Non-Hermitian Framework

Fei Wang, Guoying Liang, Zecheng Zhao +3 more

In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a $Z_2$ symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a $U(1)$ symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase are characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, this research opens a new avenue for exploring conventional quantum phase transitions that are typically vulnerable to decoherence and environmental disruption in open quantum systems.

quant-pharXiv:2511.12246•Physical review. B./Physical review. B•Nov 18, 2025•1 citation

Dynamical scaling of Loschmidt echo in non-Hermitian systems

Jia-Chen Tang, Su-Peng Kou, Gaoyong Sun

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.

arXiv:2105.05696•Europhysics Letters (EPL)•Feb 1, 2022•25 citations

Biorthogonal quantum criticality in non-Hermitian many-body systems

Gaoyong Sun, Jia-Chen Tang, Su-Peng Kou

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

arXiv:2009.11183•Frontiers of Physics•Nov 19, 2021•52 citations
In this work we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a new universality class with unusual critical exponent. We also emphasize the ability of the Loschmidt echo to characterize potential phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.
The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.
We study the quantum entanglement and quantum phase transition of the non-Hermitian anisotropic spin-12\frac{1}{2}21​ XY model and XXZ model with the staggered imaginary field by analytical methods and numerical exact diagonalization, respectively. Various entanglement measures, including concurrence, negativity, mutual information, and quantum coherence, and both biorthogonal and self-normal quantities are investigated. Both the biorthogonal and self-normal entanglement quantities, except the biorthogonal concurrence, are found to be capable of detecting the first-order and PT\mathcal{PT}PT transitions in the XXZ model, as well as the Ising and RT\mathcal{RT}RT transitions in the XY model. In addition, we introduce the unconstrained concurrence and demonstrate its effectiveness in detecting these transitions. On the other hand, the Berezinskii-Kosterlitz-Thouless (BKT) transition in the XXZ model is revealed through concurrence and negativity at small non-Hermiticity strengths. Notably, the critical points observed in the Hermitian limit evolve into exceptional points as the strength of the non-Hermiticity increases. Furthermore, we find that the first-order transition survives up to a higher non-Hermiticity strength compared to the BKT transition within the PT\mathcal{PT}PT-symmetric regime of the XXZ model.
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.
In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a Z2Z_2Z2​ symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a U(1)U(1)U(1) symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase are characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, this research opens a new avenue for exploring conventional quantum phase transitions that are typically vulnerable to decoherence and environmental disruption in open quantum systems.
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.
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.