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:2106.11934 · Physical Review A

Detection of an unbroken phase of a non-Hermitian system via a Hermitian factorization surface

Leela Ganesh Chandra Lakkaraju, Aditi Sen De

Published Nov 24, 2021• 9 citations
arXivHTMLPDF

Abstract

In the traditional quantum theory, one-dimensional quantum spin models possess a factorization surface where the ground states are fully separable and have vanishing bipartite as well as multipartite entanglement. We report that in the non-Hermitian counterpart of these models, these factorization surfaces either can predict the exceptional points where the unbroken-to-broken transition occurs or can guarantee the spectrum to be real, thereby suggesting a procedure to reveal the unbroken phase. We first analytically demonstrate it for the nearest-neighbor rotation-time- $(\mathcal{RT})$ symmetric $XY$ model with uniform and alternating transverse magnetic fields, referred to as the $iATXY$ model. Exact diagonalization techniques are then employed to establish this fact for the $\mathcal{RT}$-symmetric $XYZ$ model with short- and long-range interactions as well as for the long-range $iATXY$ model. Moreover, we show that although the factorization surface prescribes the unbroken phase of the non-Hermitian model, the bipartite nearest-neighbor entanglement at the exceptional point is nonvanishing.

DOI
10.1103/physreva.104.052222

Related papers

Detecting exceptional points through dynamics in non-Hermitian systems

Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju +1 more

Non-Hermitian rotation-time reversal $(\mathcal{RT})$-symmetric spin models possess two distinct phases, the unbroken phase in which the entire spectrum is real and the broken phase which contains complex eigenspectra, thereby indicating a transition point, referred to as an exceptional point. We report that the dynamical quantities, namely, the short- and long-time average of the Loschmidt echo, which is the overlap between the initial and the final states, and the corresponding rate function can faithfully predict the exceptional point. In particular, when the initial state is prepared as the ground state in the unbroken phase of the non-Hermitian Hamiltonian and the system is quenched to either the broken or unbroken phase, we analytically demonstrate that the rate function and the average Loschmidt echo can distinguish between the quench that occurred in the broken or the unbroken phase for the nearest-neighbor non-Hermitian $XY$ model with uniform and alternating magnetic fields, thereby indicating the exceptional point. Furthermore, we exhibit that such quantities are capable of identifying the exceptional point even in models like the non-Hermitian short- and long-range $XYZ$ model with magnetic field, which can only be solved numerically, thereby establishing it as detection criteria for recognizing exceptional points.

arXiv:2212.12403•Physical Review A•Jul 25, 2024•14 citations

Recognizing critical lines via entanglement in non-Hermitian systems

Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju +1 more

The non-Hermitian model exhibits counterintuitive phenomena that are not observed in the Hermitian counterparts. To probe the competition between non-Hermitian and Hermitian interacting components of the Hamiltonian, we focus on a system containing non-Hermitian $XY$ spin chain and Hermitian Kaplan-Shekhtman-Entin-Aharony (KSEA) interactions along with the transverse magnetic field. We show that the non-Hermitian model can be an effective Hamiltonian of a Hermitian $XX$ spin-$\frac{1}{2}$ with KSEA interaction and a local magnetic field that interacts with local and nonlocal reservoirs. The analytical expression of the energy spectrum divides the system parameters into two regimes: in one region, the strength of Hermitian KSEA interactions dominates over the imaginary non-Hermiticity parameter, while in the other, the opposite is true. In the former situation, we demonstrate that the nearest-neighbor entanglement and its derivative can identify quantum critical lines with the variation of the magnetic field. In this domain, we determine a surface where the entanglement vanishes, similar to the factorization surface, known in the Hermitian case. On the other hand, when non-Hermiticity parameters dominate, we report the exceptional and critical points where the energy gap vanishes and illustrate that bipartite entanglement is capable of detecting these transitions as well. Going beyond this scenario, when the ground state evolves after a sudden quench with the transverse magnetic field, both the rate function and the fluctuation of bipartite entanglement quantified via its second moment can detect critical lines generated without quenching dynamics.

arXiv:2305.08374•Physical Review A•Jan 5, 2026•1 citation

Non-Hermitian anisotropic XY model with intrinsic rotation-time-reversal symmetry

X. Z. Zhang, Z. Song

We systematically study the non-Hermitian version of the one-dimensional anisotropic $XY$ model, which in its original form is a unique, exactly solvable, quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has a full real spectrum if all of the eigenvectors are intrinsic rotation-time-reversal symmetric rather than parity-time-reversal symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, i.e., an isotropic $XY$ spin chain with nearest-neighbor coupling. Based on the exact solution, exceptional points which separate the unbroken- and broken-symmetry regions are obtained and lie on a hyperbola in the thermodynamic limit. This provides a nice paradigm to elucidate the complex quantum-mechanics theory for a quantum spin system.

arXiv:1210.5613•Physical Review A•Jan 16, 2013•45 citations

Crossover behavior at an exceptional point for quantum entanglement and correlation in a non-Hermitian XY spin system

Chuanzheng Miao, Yue Li, Jie Wang +5 more

Non-Hermitian spin systems have attracted extensive interest due to their unconventional magnetic properties, rich entanglement resources, and unusual quantum criticality phenomena. In this paper, based on the exact solution of a one-dimensional non-Hermitian spin-1/2 XY model with rotation-time-reversal ($\mathcal{RT}$) symmetry [X. Z. Zhang et al., Phys. Rev. A 87, 012114 (2013)], we study the ground-state energy density, magnetization, correlation functions, quantum entanglement, and correlation in $\mathcal{RT}$-symmetric and $\mathcal{RT}$-broken phases as well as their characteristics at the exceptional point. We find that the energy density rises faster with the non-Hermitian parameter $|\ensuremath{\gamma}|$ in the symmetric region than in the broken one and is elevated rapidly at the exceptional point, and the decay of magnetization has similar results. We analyze the effect of $\ensuremath{\gamma}$ on the system and find that the energy density decreases linearly with the external magnetic field $h$ for $\ensuremath{\gamma}>0,$ while it is bifurcated when $\ensuremath{\gamma}=0$. In addition, the behaviors of the energy density indicate that the phase transition caused by symmetry breaking is second order, which is further demonstrated by the magnetization, quantum entanglement, etc. The numerical results of the correlation functions surprisingly indicate that the $\mathcal{RT}$-broken phase has quasi-long-range order, which is quite different from the Hermitian XY model. Especially, the crossover behavior of the ground-state entanglement shows that it increases with $\ensuremath{\gamma}$ in the symmetric region, which is opposite to the case of the broken one, and its maximum always appears at the exceptional point. The above behaviors at the phase boundary are actually ascribed to the fierce competition between $\ensuremath{\gamma}$ and $h$, which results in a rapid decline of magnetization and the appearance of the maximum of entanglement.

Physical review. B./Physical review. B•Jul 1, 2024•10 citations

Observable signatures of exceptional points from left-right eigenstate distinction

Leela Ganesh Chandra Lakkaraju, Soumik Bandyopadhyay, Sudipto Singha Roy +1 more

Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems, a prime example being spectral singularities known as exceptional points. Their relevance in, e.g., quantum sensing, unidirectional transport, and robust lasing makes it important to be able to identify exceptional points through observable features of a many-body system. Here, using as an example a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, we develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian, which in a non-Hermitian system are no longer the adjoint of each other. We first show that a global measure constructed from the difference between the Hamiltonian and its adjoint locates exceptional points via distinct non-analytic behavior. At the level of observables, differences in local spin correlations evaluated on the right and left eigenstates provide a reliable static detection scheme. In contrast, static bipartite entanglement measures fail to capture this distinction, urging us to study the quantum dynamics of the model. Following a sudden quench, we demonstrate that the time-averaged right-left entanglement entropy difference directly encodes signatures of the exceptional point. In the RT-symmetric regime, it exhibits a pronounced peak at the exceptional point, whereas in the PT-symmetric regime it behaves as an order-parameter-like quantity, remaining finite in one phase and vanishing at the transition. Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points, providing a practical route to identify them in existing quantum simulators.

quant-pharXiv:2606.11333•Quantum Science and Technology•Jun 11, 2026•0 citations

Entanglement Negativity and Exceptional-Point Signatures in a PT-Symmetric Non-Hermitian XY Dimer: Parameter Regimes and Directional-Coupler Mapping

Linzhi Jiang, Weicheng Miao, Wen-Yang Sun +1 more

We investigate a non-Hermitian two-spin XY model driven by alternating real and imaginary transverse fields and derive an explicit analytic formula for the ground-state entanglement negativity. This provides a systematic analytic characterization of how ground-state entanglement behaves across PT-symmetry breaking in a non-Hermitian spin dimer. In the PT-symmetric regime, the anisotropy γ enhances entanglement, whereas the real field h0 suppresses it; in the PT-broken regime dominated by φ3, the negativity decreases monotonically with the imaginary field η0. Moreover, the first derivative of the negativity exhibits a cusp-type non-analyticity at the exceptional point (EP), consistent with the ground-state phase boundary and revealing a direct correspondence between entanglement transitions and exceptional-point physics. To facilitate implementation in integrated quantum photonics, we map h0,η0,γ onto the device parameters Δβ,g,κ of a PT-symmetric directional coupler and propose a two-qubit quantum state tomography readout based on local Pauli measurements, thereby offering a concrete entanglement-based probe of exceptional-point signatures in a realistic photonic platform. Within this model, we identify parameter regimes for observing this signature: a cusp feature is expected near Δβ≈0 and g≈κ, which remains observable under small detuning and moderate loss mismatch. These results offer a testable avenue for entanglement-based probing of PT-symmetry breaking and may inform device characterization and quantitative assessment in integrated quantum photonics. These combined advances provide both analytical insight into non-Hermitian entanglement structure and a feasible route toward experimentally diagnosing PT-symmetry breaking using entanglement.

Photonics•Dec 18, 2025•1 citation
In the traditional quantum theory, one-dimensional quantum spin models possess a factorization surface where the ground states are fully separable and have vanishing bipartite as well as multipartite entanglement. We report that in the non-Hermitian counterpart of these models, these factorization surfaces either can predict the exceptional points where the unbroken-to-broken transition occurs or can guarantee the spectrum to be real, thereby suggesting a procedure to reveal the unbroken phase. We first analytically demonstrate it for the nearest-neighbor rotation-time- (RT)(\mathcal{RT})(RT) symmetric XYXYXY model with uniform and alternating transverse magnetic fields, referred to as the iATXYiATXYiATXY model. Exact diagonalization techniques are then employed to establish this fact for the RT\mathcal{RT}RT-symmetric XYZXYZXYZ model with short- and long-range interactions as well as for the long-range iATXYiATXYiATXY model. Moreover, we show that although the factorization surface prescribes the unbroken phase of the non-Hermitian model, the bipartite nearest-neighbor entanglement at the exceptional point is nonvanishing.
Non-Hermitian rotation-time reversal (RT)(\mathcal{RT})(RT)-symmetric spin models possess two distinct phases, the unbroken phase in which the entire spectrum is real and the broken phase which contains complex eigenspectra, thereby indicating a transition point, referred to as an exceptional point. We report that the dynamical quantities, namely, the short- and long-time average of the Loschmidt echo, which is the overlap between the initial and the final states, and the corresponding rate function can faithfully predict the exceptional point. In particular, when the initial state is prepared as the ground state in the unbroken phase of the non-Hermitian Hamiltonian and the system is quenched to either the broken or unbroken phase, we analytically demonstrate that the rate function and the average Loschmidt echo can distinguish between the quench that occurred in the broken or the unbroken phase for the nearest-neighbor non-Hermitian XYXYXY model with uniform and alternating magnetic fields, thereby indicating the exceptional point. Furthermore, we exhibit that such quantities are capable of identifying the exceptional point even in models like the non-Hermitian short- and long-range XYZXYZXYZ model with magnetic field, which can only be solved numerically, thereby establishing it as detection criteria for recognizing exceptional points.
The non-Hermitian model exhibits counterintuitive phenomena that are not observed in the Hermitian counterparts. To probe the competition between non-Hermitian and Hermitian interacting components of the Hamiltonian, we focus on a system containing non-Hermitian XYXYXY spin chain and Hermitian Kaplan-Shekhtman-Entin-Aharony (KSEA) interactions along with the transverse magnetic field. We show that the non-Hermitian model can be an effective Hamiltonian of a Hermitian XXXXXX spin-12\frac{1}{2}21​ with KSEA interaction and a local magnetic field that interacts with local and nonlocal reservoirs. The analytical expression of the energy spectrum divides the system parameters into two regimes: in one region, the strength of Hermitian KSEA interactions dominates over the imaginary non-Hermiticity parameter, while in the other, the opposite is true. In the former situation, we demonstrate that the nearest-neighbor entanglement and its derivative can identify quantum critical lines with the variation of the magnetic field. In this domain, we determine a surface where the entanglement vanishes, similar to the factorization surface, known in the Hermitian case. On the other hand, when non-Hermiticity parameters dominate, we report the exceptional and critical points where the energy gap vanishes and illustrate that bipartite entanglement is capable of detecting these transitions as well. Going beyond this scenario, when the ground state evolves after a sudden quench with the transverse magnetic field, both the rate function and the fluctuation of bipartite entanglement quantified via its second moment can detect critical lines generated without quenching dynamics.
We systematically study the non-Hermitian version of the one-dimensional anisotropic XYXYXY model, which in its original form is a unique, exactly solvable, quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has a full real spectrum if all of the eigenvectors are intrinsic rotation-time-reversal symmetric rather than parity-time-reversal symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, i.e., an isotropic XYXYXY spin chain with nearest-neighbor coupling. Based on the exact solution, exceptional points which separate the unbroken- and broken-symmetry regions are obtained and lie on a hyperbola in the thermodynamic limit. This provides a nice paradigm to elucidate the complex quantum-mechanics theory for a quantum spin system.
Non-Hermitian spin systems have attracted extensive interest due to their unconventional magnetic properties, rich entanglement resources, and unusual quantum criticality phenomena. In this paper, based on the exact solution of a one-dimensional non-Hermitian spin-1/2 XY model with rotation-time-reversal (RT\mathcal{RT}RT) symmetry [X. Z. Zhang et al., Phys. Rev. A 87, 012114 (2013)], we study the ground-state energy density, magnetization, correlation functions, quantum entanglement, and correlation in RT\mathcal{RT}RT-symmetric and RT\mathcal{RT}RT-broken phases as well as their characteristics at the exceptional point. We find that the energy density rises faster with the non-Hermitian parameter $|\ensuremath{\gamma}|$ in the symmetric region than in the broken one and is elevated rapidly at the exceptional point, and the decay of magnetization has similar results. We analyze the effect of $\ensuremath{\gamma}$ on the system and find that the energy density decreases linearly with the external magnetic field hhh for $\ensuremath{\gamma}>0,$ while it is bifurcated when $\ensuremath{\gamma}=0$. In addition, the behaviors of the energy density indicate that the phase transition caused by symmetry breaking is second order, which is further demonstrated by the magnetization, quantum entanglement, etc. The numerical results of the correlation functions surprisingly indicate that the RT\mathcal{RT}RT-broken phase has quasi-long-range order, which is quite different from the Hermitian XY model. Especially, the crossover behavior of the ground-state entanglement shows that it increases with $\ensuremath{\gamma}$ in the symmetric region, which is opposite to the case of the broken one, and its maximum always appears at the exceptional point. The above behaviors at the phase boundary are actually ascribed to the fierce competition between $\ensuremath{\gamma}$ and hhh, which results in a rapid decline of magnetization and the appearance of the maximum of entanglement.
Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems, a prime example being spectral singularities known as exceptional points. Their relevance in, e.g., quantum sensing, unidirectional transport, and robust lasing makes it important to be able to identify exceptional points through observable features of a many-body system. Here, using as an example a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, we develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian, which in a non-Hermitian system are no longer the adjoint of each other. We first show that a global measure constructed from the difference between the Hamiltonian and its adjoint locates exceptional points via distinct non-analytic behavior. At the level of observables, differences in local spin correlations evaluated on the right and left eigenstates provide a reliable static detection scheme. In contrast, static bipartite entanglement measures fail to capture this distinction, urging us to study the quantum dynamics of the model. Following a sudden quench, we demonstrate that the time-averaged right-left entanglement entropy difference directly encodes signatures of the exceptional point. In the RT-symmetric regime, it exhibits a pronounced peak at the exceptional point, whereas in the PT-symmetric regime it behaves as an order-parameter-like quantity, remaining finite in one phase and vanishing at the transition. Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points, providing a practical route to identify them in existing quantum simulators.
We investigate a non-Hermitian two-spin XY model driven by alternating real and imaginary transverse fields and derive an explicit analytic formula for the ground-state entanglement negativity. This provides a systematic analytic characterization of how ground-state entanglement behaves across PT-symmetry breaking in a non-Hermitian spin dimer. In the PT-symmetric regime, the anisotropy γ enhances entanglement, whereas the real field h0 suppresses it; in the PT-broken regime dominated by φ3, the negativity decreases monotonically with the imaginary field η0. Moreover, the first derivative of the negativity exhibits a cusp-type non-analyticity at the exceptional point (EP), consistent with the ground-state phase boundary and revealing a direct correspondence between entanglement transitions and exceptional-point physics. To facilitate implementation in integrated quantum photonics, we map h0,η0,γ onto the device parameters Δβ,g,κ of a PT-symmetric directional coupler and propose a two-qubit quantum state tomography readout based on local Pauli measurements, thereby offering a concrete entanglement-based probe of exceptional-point signatures in a realistic photonic platform. Within this model, we identify parameter regimes for observing this signature: a cusp feature is expected near Δβ≈0 and g≈κ, which remains observable under small detuning and moderate loss mismatch. These results offer a testable avenue for entanglement-based probing of PT-symmetry breaking and may inform device characterization and quantitative assessment in integrated quantum photonics. These combined advances provide both analytical insight into non-Hermitian entanglement structure and a feasible route toward experimentally diagnosing PT-symmetry breaking using entanglement.