pith. sign in

arxiv: 2606.11333 · v1 · pith:NMYQJOIUnew · submitted 2026-06-09 · 🪐 quant-ph · cond-mat.quant-gas· cond-mat.str-el

Observable signatures of exceptional points from left-right eigenstate distinction

Leela Ganesh Chandra Lakkaraju , Soumik Bandyopadhyay , Sudipto Singha Roy , Philipp Hauke This is my paper

Pith reviewed 2026-06-27 13:13 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gascond-mat.str-el
keywords non-Hermitian systemsexceptional pointsleft and right eigenvectorsspin correlationsentanglement entropyPT symmetryRT symmetryquantum spin chains
0
0 comments X

The pith

Differences between left and right eigenstates detect exceptional points through spin correlations and entanglement dynamics in non-Hermitian spin chains.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework for detecting exceptional points in non-Hermitian many-body systems by exploiting the distinction between left and right eigenvectors, which are not adjoints of each other. In a one-dimensional complex XY spin chain realizing both RT- and PT-symmetric regimes, differences in local spin correlations between these eigenvectors serve as a static detection method. After a sudden quench, the time-averaged difference in right-left entanglement entropy encodes the exceptional point, showing a pronounced peak in the RT regime and order-parameter-like behavior in the PT regime. This establishes a direct connection between non-Hermitian eigenstate structure and observable signatures.

Core claim

In a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, differences between left and right eigenvectors of the non-Hermitian Hamiltonian produce observable signatures of exceptional points. A global measure from the Hamiltonian minus its adjoint shows non-analytic behavior at these points. Local spin correlation differences provide static detection, while the time-averaged right-left entanglement entropy difference after a quench peaks at the exceptional point in the RT regime and remains finite in one PT phase before vanishing at the transition.

What carries the argument

The distinction between left and right eigenvectors of the non-Hermitian Hamiltonian, used to build differences in local spin correlations and time-averaged entanglement entropy that locate exceptional points.

If this is right

  • Local spin correlations on right versus left eigenstates detect exceptional points without requiring time evolution.
  • The time-averaged right-left entanglement entropy difference peaks sharply at the exceptional point in the RT-symmetric regime.
  • In the PT-symmetric regime the same entanglement difference stays finite away from the exceptional point and drops to zero at the transition.
  • The approach supplies a practical route to identify exceptional points using existing quantum simulators.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental techniques to prepare or measure left eigenstates would allow direct use of these static and dynamic signatures.
  • The framework could extend to other non-Hermitian lattice models that host exceptional points under similar symmetries.
  • The order-parameter behavior in the PT regime suggests a possible link between exceptional points and dynamical phase transitions in open systems.

Load-bearing premise

Left and right eigenstates remain experimentally distinguishable with their correlation and entanglement differences surviving without being erased by decoherence or measurement back-action.

What would settle it

An experiment that prepares states approximating the left and right eigenstates and finds no peak in the time-averaged entanglement entropy difference or no distinction in spin correlations at the parameter value predicted to host the exceptional point would falsify the signatures.

Figures

Figures reproduced from arXiv: 2606.11333 by Leela Ganesh Chandra Lakkaraju, Philipp Hauke, Soumik Bandyopadhyay, Sudipto Singha Roy.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The Hamiltonian-based quantifier [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The Hamiltonian-based quantifier [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Observable-based quantifiers defined in Eq. (15) in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Observable-based quantifiers defined in Eq. (15) in the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time-averaged entanglement entropy difference [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dynamical entanglement entropy difference [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript develops a framework for detecting exceptional points (EPs) in non-Hermitian many-body systems using a one-dimensional complex XY spin chain that realizes both RT-symmetric and PT-symmetric regimes. It shows that a global measure based on the difference between the Hamiltonian and its adjoint exhibits non-analytic behavior at EPs; differences in local spin correlations evaluated on left versus right eigenstates provide static signatures; and, following a quench, the time-averaged right-left entanglement entropy difference encodes EP signatures, manifesting as a peak in the RT regime and order-parameter-like behavior (finite in one phase, vanishing at the transition) in the PT regime.

Significance. If the derivations and numerics hold, the work establishes a direct link between non-Hermitian eigenstate structure and experimentally relevant observables, offering a route to EP detection in quantum simulators. Credit is due for the explicit model, the regime-specific analysis, and the use of quench dynamics to extract signatures that static entanglement measures miss.

major comments (1)
  1. [Abstract and quench-dynamics section] Abstract and § on quench dynamics: the central claim that the time-averaged right-left entanglement entropy difference 'directly encodes signatures of the exceptional point' and provides a 'practical route' assumes left and right eigenstates remain distinguishable under realistic conditions, yet the manuscript contains no preparation/readout protocols for left eigenvectors and no open-system (e.g., Lindblad) analysis to verify that decoherence or measurement back-action does not erase the reported peak or order-parameter behavior. This is load-bearing for the observability assertions.
minor comments (1)
  1. Notation for left and right eigenvectors and the precise definition of the time-averaged entanglement difference should be stated explicitly with equation numbers in the methods or results section to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed report and address the single major comment below. Our response clarifies the scope of the theoretical claims without altering the manuscript.

read point-by-point responses

  1. Referee: [Abstract and quench-dynamics section] Abstract and § on quench dynamics: the central claim that the time-averaged right-left entanglement entropy difference 'directly encodes signatures of the exceptional point' and provides a 'practical route' assumes left and right eigenstates remain distinguishable under realistic conditions, yet the manuscript contains no preparation/readout protocols for left eigenvectors and no open-system (e.g., Lindblad) analysis to verify that decoherence or measurement back-action does not erase the reported peak or order-parameter behavior. This is load-bearing for the observability assertions.

    Authors: The manuscript is a theoretical study that derives signatures of exceptional points from the left-right eigenstate distinction in an ideal non-Hermitian many-body system. The abstract and quench-dynamics section state that the time-averaged entanglement-entropy difference encodes these signatures within the closed-system dynamics; they do not assert that left and right eigenvectors are immediately distinguishable in the presence of realistic decoherence or that explicit experimental protocols are provided. We agree that no preparation/readout protocols or Lindblad analysis appear in the work. Such elements would require additional assumptions about the noise model and experimental platform and lie outside the paper's scope. The reported peak and order-parameter-like behavior are therefore presented as ideal-case observables that can serve as targets for future simulator implementations. Because the claims remain accurately scoped to the closed-system framework, we do not consider revisions necessary. revision: no

Circularity Check

0 steps flagged

No circularity: explicit model computations independent of inputs

full rationale

The paper constructs signatures from the left-right eigenstate distinction in an explicitly defined RT/PT-symmetric XY chain. The global measure uses H - H†, local correlations are evaluated directly on the eigenstates, and the quench dynamics computes time-averaged entanglement differences. No equations reduce by construction to fitted parameters, self-citations, or ansatzes; all steps are independent calculations on the stated Hamiltonian. This matches the default expectation of a non-circular theoretical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the model is presented as a standard complex XY chain realizing known symmetry classes.

pith-pipeline@v0.9.1-grok · 5828 in / 1138 out tokens · 19706 ms · 2026-06-27T13:13:36.283433+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    and increases monotonically with the field strength, as il- lustrated in the first panel of Fig. 2(a). The first derivative DPT ′ =dD PT /dhPT remains continuous and smooth across the exceptional point (see Fig. 2 (b)) in contrast to theRTtran- sition. Instead, the exceptional signature is pushed to a higher order. Evaluating thesecond derivativeD PT ′′ =...

  2. [2]

    This choice is natural in non-Hermitian set- tings, where non-unitary evolution under the Hamiltonian and its adjoint prepares distinct right and left ensembles [20, 21]

    typically introduced in non-Hermitian systems to define expectation values, we instead evaluate observables directly with respect to the independent right and left ground-state man- ifolds [34, 35]. This choice is natural in non-Hermitian set- tings, where non-unitary evolution under the Hamiltonian and its adjoint prepares distinct right and left ensembl...

    2024

  3. [3]

    Kato,Perturbation Theory for Linear Operators(Springer, New York, 1966)

    T. Kato,Perturbation Theory for Linear Operators(Springer, New York, 1966)

    1966

  4. [4]

    W. D. Heiss, The physics of exceptional points, J Phys A: Math Theor45, 444016 (2012)

    2012

  5. [5]

    Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Unidirectional invisibility induced by PT-symmetric periodic structures, Physical Review Letters 106, 213901 (2011)

    2011

  6. [6]

    Feng, Y.-L

    L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Experi- mental demonstration of a unidirectional reflectionless parity- time metamaterial at optical frequencies, Nature Materials12, 108 (2013)

    2013

  7. [7]

    Longhi,PT-symmetric laser absorber, Physical Review A 82, 031801 (2010)

    S. Longhi,PT-symmetric laser absorber, Physical Review A 82, 031801 (2010)

    2010

  8. [8]

    Y. D. Chong, L. Ge, and A. D. Stone,PT-symmetry breaking and laser-absorber modes in optical scattering systems, Physical Review Letters106, 093902 (2011)

    2011

  9. [9]

    Harari, M

    G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science359, eaar4003 (2018)

    2018

  10. [10]

    M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insu- lator laser: Experiments, Science359, eaar4005 (2018)

    2018

  11. [11]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El- Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature548, 187 (2017)

    2017

  12. [12]

    Chen, S ¸

    W. Chen, S ¸. Kaya¨Ozdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature548, 192 (2017)

    2017

  13. [13]

    K. D. Agarwal, T. K. Konar, L. G. C. Lakkaraju, and A. S. De, Critical quantum metrology using non-hermitian spin model with rt-symmetry (2025), arXiv:2503.24331 [quant-ph]

    work page arXiv 2025

  14. [14]

    K. D. Agarwal, T. K. Konar, L. G. C. Lakkaraju, and A. S. De, Quantum-enhanced sensing from the interplay of long-range interactions and non-hermiticity (2026), arXiv:2605.01912 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  15. [15]

    T. K. Konar, L. G. C. Lakkaraju, and A. Sen (De), Quantum battery with non-hermitian charging, Phys. Rev. A109, 042207 (2024)

    2024

  16. [16]

    Moiseyev, Non-hermitian quantum mechanics, Physics Re- ports302, 212 (1998)

    N. Moiseyev, Non-hermitian quantum mechanics, Physics Re- ports302, 212 (1998)

    1998

  17. [17]

    R. H. Dicke, Coherence in spontaneous radiation processes, Physical Review93, 99 (1954)

    1954

  18. [18]

    Facchi and S

    P. Facchi and S. Pascazio, Quantum zeno dynamics: mathemat- ical and physical aspects, Journal of Physics A: Mathematical and Theoretical41, 493001 (2008)

    2008

  19. [19]

    K. T. Geier and P. Hauke, From non-hermitian linear response to dynamical correlations and fluctuation-dissipation relations in quantum many-body systems, PRX Quantum3, 030308 (2022)

    2022

  20. [20]

    K. T. Geier, J. Reichstetter, and P. Hauke, Non-invasive mea- surement of currents in analog quantum simulators (2021), arXiv:2106.12599 [quant-ph]

    work page arXiv 2021

  21. [21]

    Ashida, S

    Y. Ashida, S. Furukawa, and M. Ueda, Parity-time-symmetric quantum critical phenomena, Nature Communications8, 15791 (2017)

    2017

  22. [22]

    Bandyopadhyay, P

    S. Bandyopadhyay, P. Hauke, and S. Singha Roy, Quantifying non-hermiticity using single- and many-particle quantum prop- erties, Phys. Rev. B112, 134201 (2025)

    2025

  23. [23]

    Singha Roy, S

    S. Singha Roy, S. Bandyopadhyay, R. Costa de Almeida, and P. Hauke, Unveiling eigenstate thermalization for non-hermitian systems, Phys. Rev. Lett.134, 180405 (2025)

    2025

  24. [24]

    X. Z. Zhang and Z. Song, Non-hermitian anisotropicxymodel with intrinsic rotation-time-reversal symmetry, Phys. Rev. A87, 012114 (2013)

    2013

  25. [25]

    T. E. Lee and C.-K. Chan, Heralded magnetism in non-hermitian atomic systems, Phys. Rev. X4, 041001 (2014)

    2014

  26. [26]

    Pi and R

    J. Pi and R. L¨ u, Phase diagram and quantum criticality of a non- hermitian xy model with a complex transverse field, Journal of Physics: Condensed Matter33, 345601 (2021)

    2021

  27. [27]

    D. C. Liu and M. T. Batchelor, Characterizing phase transitions and criticality in non-hermitian extensions of the xy model, Phys. Rev. B112, 014422 (2025)

    2025

  28. [28]

    Das Agarwal, T

    K. Das Agarwal, T. K. Konar, L. G. C. Lakkaraju, and A. Sen(De), Recognizing critical lines via entanglement in non- hermitian systems, Phys. Rev. A113, 022201 (2026)

    2026

  29. [29]

    Jordan and E

    P. Jordan and E. P. Wigner, ¨ uber das paulische¨aquivalenzverbot, inThe Collected Works of Eugene Paul Wigner(Springer, 1993) pp. 109–129

    1993

  30. [30]

    Barouch, B

    E. Barouch, B. M. McCoy, and M. Dresden, Statistical mechan- ics of theXYmodel. i, Phys. Rev. A2, 1075 (1970)

    1970

  31. [31]

    G. B. Mbeng, A. Russomanno, and G. E. Santoro, The quantum Ising chain for beginners, SciPost Phys. Lect. Notes , 82 (2024)

    2024

  32. [32]

    C. M. Bender, Making sense of non-hermitian hamiltonians, Reports on Progress in Physics70, 947 (2007)

    2007

  33. [33]

    C. M. Bender and S. Boettcher, Real spectra in non-hermitian hamiltonians havingPTsymmetry, Phys. Rev. Lett.80, 5243 (1998)

    1998

  34. [34]

    B. Zhu, Y. Ke, H. Zhong, and C. Lee, Dynamic winding number for exploring band topology, Phys. Rev. Res.2, 023043 (2020)

    2020

  35. [35]

    D. C. Brody, Biorthogonal quantum mechanics, Journal of Physics A: Mathematical and Theoretical47, 035305 (2013)

    2013

  36. [36]

    Turkeshi and M

    X. Turkeshi and M. Schir ´o, Entanglement and correlation spreading in non-hermitian spin chains, Phys. Rev. B107, L020403 (2023)

    2023

  37. [37]

    Turkeshi, M

    X. Turkeshi, M. Dalmonte, R. Fazio, and M. Schir `o, Entan- glement transitions from stochastic resetting of non-hermitian quasiparticles, Phys. Rev. B105, L241114 (2022)

    2022

  38. [38]

    Zhang and J

    H. Zhang and J. Jin, Parameter estimation with the steady states of non-hermitian spin chains, Physica A: Statistical Mechanics and its Applications599, 127460 (2022)

    2022

  39. [39]

    R. D. Soares, Y. L. Gal, C. Y. Leung, D. Meidan, A. Romito, and M. Schir`o, Symmetries, conservation laws and entanglement in non-Hermitian fermionic lattices, SciPost Phys.19, 094 (2025)

    2025

  40. [40]

    Titum, J

    P. Titum, J. T. Iosue, J. R. Garrison, A. V. Gorshkov, and Z.-X. Gong, Probing ground-state phase transitions through quench dynamics, Phys. Rev. Lett.123, 115701 (2019)

    2019

  41. [41]

    W.-C. Gao, C. Zheng, L. Liu, T.-J. Wang, and C. Wang, Experi- mental simulation of the parity-time symmetric dynamics using photonic qubits, Opt. Express29, 517 (2021)

    2021

  42. [42]

    Y. Wu, W. Liu, J. Geng, X. Song, X. Ye, C.-K. Duan, X. Rong, and J. Du, Observation of parity-time symmetry breaking in a single-spin system, Science364, 878 (2019)

    2019

  43. [43]

    L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, and P. Xue, Observation of topological edge states in parity-time-symmetric quantum walks, Nat Phys13, 1117 (2017)

    2017

  44. [44]

    Tang, Y.-T

    J.-S. Tang, Y.-T. Wang, S. Yu, D.-Y. He, J.-S. Xu, B.-H. Liu, G. Chen, Y.-N. Sun, K. Sun, Y.-J. Han,et al., Experimental 14 investigation of the no-signalling principle in parity–time sym- metric theory using an open quantum system, Nature Photonics 10, 642 (2016)

    2016

  45. [45]

    J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, and L. Luo, Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat Commun10, 855 (2019)

    2019

  46. [46]

    J. Wen, C. Zheng, X. Kong, S. Wei, T. Xin, and G. Long, Experimental demonstration of a digital quantum simulation of a generalPT-symmetric system, Phys. Rev. A99, 062122 (2019)

    2019

  47. [47]

    Non-Hermitian Hamiltonian engineering in qudit systems, M. M. Wauters, P. Boschetto, E. Ballini, A. Biella and P. Hauke, will be available in arXiv soon

  48. [48]

    Vidal, J

    G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in quantum critical phenomena, Phys. Rev. Lett.90, 227902 (2003)

    2003

  49. [49]

    Calabrese and J

    P. Calabrese and J. Cardy, Entanglement entropy and quantum field theory, Journal of Statistical Mechanics: Theory and Ex- periment2004, P06002 (2004)

    2004

  50. [50]

    Peschel, Calculation of reduced density matrices from correla- tion functions, Journal of Physics A: Mathematical and General 36, L205 (2003)

    I. Peschel, Calculation of reduced density matrices from correla- tion functions, Journal of Physics A: Mathematical and General 36, L205 (2003)

    2003

  51. [51]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, 2007)

    2007

  52. [52]

    J. F. Poyatos, J. I. Cirac, and P. Zoller, Quantum reservoir engi- neering with laser cooled trapped ions, Phys. Rev. Lett.77, 4728 (1996)

    1996

  53. [53]

    Sannia, R

    A. Sannia, R. Mart ´ınez-Pe˜na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Dissipation as a resource for Quantum Reservoir Computing, Quantum8, 1291 (2024)

    2024

  54. [54]

    Metelmann and A

    A. Metelmann and A. A. Clerk, Nonreciprocal photon transmis- sion and amplification via reservoir engineering, Phys. Rev. X 5, 021025 (2015)

    2015

  55. [55]

    M. Keck, D. Rossini, and R. Fazio, Persistent currents by reser- voir engineering, Phys. Rev. A98, 053812 (2018)

    2018

  56. [56]

    M. B. Plenio and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Rev. Mod. Phys.70, 101 (1998)

    1998

  57. [57]

    A. J. Daley, Quantum trajectories and open many-body quantum systems, Advances in Physics63, 77 (2014), https://doi.org/10.1080/00018732.2014.933502

    work page doi:10.1080/00018732.2014.933502 2014

  58. [58]

    Turkeshi, A

    X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schir ´o, Measurement-induced entanglement transitions in the quantum ising chain: From infinite to zero clicks, Phys. Rev. B103, 224210 (2021)

    2021