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  • Letter
  • Open Access

Finite steady-state current defies non-Hermitian many-body localization

Pietro Brighi1, Marko Ljubotina2,3,4, Federico Roccati5,6, and Federico Balducci7,*

  • *Contact author: fbalducci@pks.mpg.de
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Phys. Rev. Research 7, L042014 – Published 14 October, 2025

DOI: https://doi.org/10.1103/crwj-x7j8

Abstract

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a noncommutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understanding localization in non-Hermitian settings.

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References (74)

  1. Z. G. Y. Ashida and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  2. F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps, Phys. Rev. A 100, 062131 (2019).
  3. A. N. Poddubny, Interaction-induced analog of a non-Hermitian skin effect in a lattice two-body problem, Phys. Rev. B 107, 045131 (2023).
  4. L. Garbe, Y. Minoguchi, J. Huber, and P. Rabl, The bosonic skin effect: Boundary condensation in asymmetric transport, SciPost Phys. 16, 029 (2024).
  5. J. Gliozzi, G. De Tomasi, and T. L. Hughes, Many-body non-Hermitian skin effect for multipoles, Phys. Rev. Lett. 133, 136503 (2024).
  6. S. Wang, B. Wang, C. Liu, C. Qin, L. Zhao, W. Liu, S. Longhi, and P. Lu, Nonlinear non-Hermitian skin effect and skin solitons in temporal photonic feedback lattices, Phys. Rev. Lett. 134, 243805 (2025).
  7. A. Felski and F. K. Kunst, Exceptional points and stability in nonlinear models of population dynamics having PT symmetry, Phys. Rev. Res. 7, 013326 (2025).
  8. N. H. Kwong, J. Wingenbach, L. Ares, J. Sperling, X. Ma, S. Schumacher, and R. Binder, Universal neighborhood topology and geometry of exceptional points in physical systems, arXiv:2502.19236.
  9. R. Hamazaki, K. Kawabata, and M. Ueda, Non-Hermitian many-body localization, Phys. Rev. Lett. 123, 090603 (2019).
  10. I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interacting electrons in disordered wires: Anderson localization and low-T transport, Phys. Rev. Lett. 95, 206603 (2005).
  11. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states, Ann. Phys. 321, 1126 (2006).
  12. M. Serbyn, Z. Papić, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states, Phys. Rev. Lett. 111, 127201 (2013).
  13. V. Ros, M. Müller, and A. Scardicchio, Integrals of motion in the many-body localized phase, Nucl. Phys. B 891, 420 (2015).
  14. J. Z. Imbrie, Diagonalization and many-body localization for a disordered quantum spin chain, Phys. Rev. Lett. 117, 027201 (2016); On many-body localization for quantum spin chains, J. Stat. Phys. 163, 998 (2016).
  15. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Colloquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys. 91, 021001 (2019).
  16. P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Zakrzewski, Many-body localization in the age of classical computing, Rep. Prog. Phys. 88, 026502 (2025).
  17. V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
  18. M. Žnidarič, T. Prosen, and P. Prelovšek, Many-body localization in the Heisenberg XXZ magnet in a random field, Phys. Rev. B 77, 064426 (2008).
  19. A. Pal and D. A. Huse, Many-body localization phase transition, Phys. Rev. B 82, 174411 (2010).
  20. A. D. Luca and A. Scardicchio, Ergodicity breaking in a model showing many-body localization, Europhys. Lett. 101, 37003 (2013).
  21. D. J. Luitz, N. Laflorencie, and F. Alet, Many-body localization edge in the random-field Heisenberg chain, Phys. Rev. B 91, 081103 (2015).
  22. R. Nandkishore, S. Gopalakrishnan, and D. A. Huse, Spectral features of a many-body-localized system weakly coupled to a bath, Phys. Rev. B 90, 064203 (2014).
  23. S. Gopalakrishnan and R. Nandkishore, Mean-field theory of nearly many-body localized metals, Phys. Rev. B 90, 224203 (2014).
  24. D. A. Huse, R. Nandkishore, F. Pietracaprina, V. Ros, and A. Scardicchio, Localized systems coupled to small baths: From Anderson to Zeno, Phys. Rev. B 92, 014203 (2015).
  25. S. Johri, R. Nandkishore, and R. N. Bhatt, Many-body localization in imperfectly isolated quantum systems, Phys. Rev. Lett. 114, 117401 (2015).
  26. M. H. Fischer, M. Maksymenko, and E. Altman, Dynamics of a many-body-localized system coupled to a bath, Phys. Rev. Lett. 116, 160401 (2016).
  27. E. Levi, M. Heyl, I. Lesanovsky, and J. P. Garrahan, Robustness of many-body localization in the presence of dissipation, Phys. Rev. Lett. 116, 237203 (2016).
  28. M. V. Medvedyeva, T. Prosen, and M. Žnidarič, Influence of dephasing on many-body localization, Phys. Rev. B 93, 094205 (2016).
  29. R. Nandkishore and S. Gopalakrishnan, Many body localized systems weakly coupled to baths, Ann. Phys. 529, 1600181 (2017).
  30. D. J. Luitz, F. Huveneers, and W. De Roeck, How a small quantum bath can thermalize long localized chains, Phys. Rev. Lett. 119, 150602 (2017).
  31. B. Everest, I. Lesanovsky, J. P. Garrahan, and E. Levi, Role of interactions in a dissipative many-body localized system, Phys. Rev. B 95, 024310 (2017).
  32. L.-N. Wu, A. Schnell, G. D. Tomasi, M. Heyl, and A. Eckardt, Describing many-body localized systems in thermal environments, New J. Phys. 21, 063026 (2019).
  33. E. Wybo, M. Knap, and F. Pollmann, Entanglement dynamics of a many-body localized system coupled to a bath, Phys. Rev. B 102, 064304 (2020).
  34. P. Brighi, A. A. Michailidis, D. A. Abanin, and M. Serbyn, Propagation of many-body localization in an Anderson insulator, Phys. Rev. B 105, L220203 (2022).
  35. N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996); Vortex pinning and non-Hermitian quantum mechanics, Phys. Rev. B 56, 8651 (1997); Non-Hermitian delocalization and eigenfunctions, 58, 8384 (1998).
  36. J. Gliozzi, F. Balducci, T. L. Hughes, and G. D. Tomasi, Non-Hermitian multipole skin effects challenge localization, arXiv:2504.10580.
  37. L.-J. Zhai, S. Yin, and G.-Y. Huang, Many-body localization in a non-Hermitian quasiperiodic system, Phys. Rev. B 102, 064206 (2020).
  38. K. Suthar, Y.-C. Wang, Y.-P. Huang, H. H. Jen, and J.-S. You, Non-Hermitian many-body localization with open boundaries, Phys. Rev. B 106, 064208 (2022).
  39. S. Ghosh, S. Gupta, and M. Kulkarni, Spectral properties of disordered interacting non-Hermitian systems, Phys. Rev. B 106, 134202 (2022).
  40. K. Yamamoto and R. Hamazaki, Localization properties in disordered quantum many-body dynamics under continuous measurement, Phys. Rev. B 107, L220201 (2023).
  41. H.-Z. Li, X.-J. Yu, and J.-X. Zhong, Non-Hermitian Stark many-body localization, Phys. Rev. A 108, 043301 (2023).
  42. J. Mák, M. J. Bhaseen, and A. Pal, Statics and dynamics of non-Hermitian many-body localization, Commun. Phys. 7, 92 (2024).
  43. G. De Tomasi and I. M. Khaymovich, Stable many-body localization under random continuous measurements in the no-click limit, Phys. Rev. B 109, 174205 (2024).
  44. G. Akemann, F. Balducci, A. Chenu, P. Päßler, F. Roccati, and R. Shir, Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking, Phys. Rev. Res. 7, 013098 (2025).
  45. F. Roccati, F. Balducci, R. Shir, and A. Chenu, Diagnosing non-Hermitian many-body localization and quantum chaos via singular value decomposition, Phys. Rev. B 109, L140201 (2024).
  46. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
  47. W. D. Roeck, L. Giacomin, F. Huveneers, and O. Prosniak, Absence of normal heat conduction in strongly disordered interacting quantum chains, arXiv:2408.04338.
  48. A. Panda and S. Banerjee, Entanglement in nonequilibrium steady states and many-body localization breakdown in a current-driven system, Phys. Rev. B 101, 184201 (2020).
  49. G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003).
  50. S. E. Begg and R. Hanai, Quantum criticality in open quantum spin chains with nonreciprocity, Phys. Rev. Lett. 132, 120401 (2024).
  51. A. Metelmann and A. A. Clerk, Nonreciprocal photon transmission and amplification via reservoir engineering, Phys. Rev. X 5, 021025 (2015).
  52. C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Topological framework for directional amplification in driven-dissipative cavity arrays, Nat. Commun. 11, 3149 (2020).
  53. D. Porras and S. Fernández-Lorenzo, Topological amplification in photonic lattices, Phys. Rev. Lett. 122, 143901 (2019).
  54. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Quantum chaos challenges many-body localization, Phys. Rev. E 102, 062144 (2020).
  55. R. K. Panda, A. Scardicchio, M. Schulz, S. R. Taylor, and M. Žnidarič, Can we study the many-body localisation transition? Europhys. Lett. 128, 67003 (2020).
  56. D. Abanin, J. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Ann. Phys. 427, 168415 (2021).
  57. P. J. D. Crowley and A. Chandran, A constructive theory of the numerically accessible many-body localized to thermal crossover, SciPost Phys. 12, 201 (2022).
  58. A. Morningstar, L. Colmenarez, V. Khemani, D. J. Luitz, and D. A. Huse, Avalanches and many-body resonances in many-body localized systems, Phys. Rev. B 105, 174205 (2022).
  59. P. J. D. Crowley and A. Chandran, Mean-field theory of failed thermalizing avalanches, Phys. Rev. B 106, 184208 (2022).
  60. D. M. Long, P. J. D. Crowley, V. Khemani, and A. Chandran, Phenomenology of the prethermal many-body localized regime, Phys. Rev. Lett. 131, 106301 (2023).
  61. Due to our conventions of ı’s, the states with positive imaginary eigenenergies are amplified, while those with negative imaginary eigenenergies are suppressed.
  62. K. Kawabata, T. Numasawa, and S. Ryu, Entanglement phase transition induced by the non-Hermitian skin effect, Phys. Rev. X 13, 021007 (2023).
  63. D. E. Mahoney and J. Richter, Transport and integrability-breaking in non-Hermitian many-body quantum systems, Phys. Rev. B 110, 134302 (2024).
  64. M. Naghiloo, M. Abbasi, Y. N. Joglekar, and K. W. Murch, Quantum state tomography across the exceptional point in a single dissipative qubit, Nat. Phys. 15, 1232 (2019).
  65. J. Cuerda, J. M. Taskinen, N. Källman, L. Grabitz, and P. Törmä, Observation of quantum metric and non-Hermitian Berry curvature in a plasmonic lattice, Phys. Rev. Res. 6, L022020 (2024).
  66. F. Pietracaprina, N. Macé, D. J. Luitz, and F. Alet, Shift-invert diagonalization of large many-body localizing spin chains, SciPost Phys. 5, 045 (2018).
  67. P. Sierant, M. Lewenstein, and J. Zakrzewski, Polynomially filtered exact diagonalization approach to many-body localization, Phys. Rev. Lett. 125, 156601 (2020).
  68. See Supplemental Material at http://link.aps.org/supplemental/10.1103/crwj-x7j8 for additional information on the numerical procedures.
  69. V. Oganesyan, A. Pal, and D. A. Huse, Energy transport in disordered classical spin chains, Phys. Rev. B 80, 115104 (2009).
  70. M. Žnidarič and M. Ljubotina, Interaction instability of localization in quasiperiodic systems, Proc. Natl. Acad. Sci. USA 115, 4595 (2018).
  71. T. Scoquart, I. V. Gornyi, and A. D. Mirlin, Role of Fock-space correlations in many-body localization, Phys. Rev. B 109, 214203 (2024).
  72. J. Niedda, G. B. Testasecca, G. Magnifico, F. Balducci, C. Vanoni, and A. Scardicchio, Renormalization-group analysis of the many-body localization transition in the random-field XXZ chain, Phys. Rev. B 112, 144201 (2025).
  73. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  74. Visit http://doi.org/10.5281/zenodo.17118846 for all the data necessary to reproduce figures.

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Phys. Rev. Research 7, L042014– Published 14 October, 2025
  • Received 14 April 2025
  • Revised 10 July 2025
  • Accepted 12 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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