Disorder-Induced Entanglement Phase Transitions in Non-Hermitian Systems with Skin Effects
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AbstractNon-Hermitian dynamics is ubiquitous in various physical systems. While recent study shows that such a dynamics leads to an area-law scaling of the entanglement entropy due to the non-Hermitian skin effects, it remains unclear how disorder changes the behavior of the entanglement entropy in a non-Hermitian system with skin effects. Here we study the dynamics of a many-body state of free fermions in the paradigmatic Hatano-Nelson model with open boundaries, and find that the area-law behavior of the entanglement entropy in the pristine Hatano-Nelson model develops into a logarithmic scaling for small disorder strength. As we further increase the disorder strength, the system reenters an area-law regime through an entanglement phase transition. At the critical point, the entanglement entropy exhibits a universal algebraic scaling. We further demonstrate the absence of a conformal invariance in the log-law regime by examining the subsystem entanglement entropy, the connected correlation function and the mutual information. Finally, we show the existence of disorder induced entanglement phase transitions in the Hatano-Nelson model with periodic boundaries.Featured image: (a) Entanglement phase diagram of the disordered Hatano-Nelson model under open boundary conditions, showing log-law and area-law regimes separated by a phase boundary with algebraic entanglement scaling. (b) Half-system entanglement entropy $S_{L/2}$ versus system size $L$ for different disorder strengths at $\gamma=-0.5$. At the critical point $W=3.35$, $S_{L/2}\propto L^{0.5}$.Popular summaryNon-Hermitian skin effects can inhibit entanglement growth, resulting in area-law entanglement in the absence of disorder. Disorder can induce Anderson localization, which also suppresses entanglement growth. Since both mechanisms suppress entanglement, one might expect the area-law behavior to persist as disorder is introduced. In this work, we study the dynamics of a half-filled many-body state in the disordered Hatano-Nelson model with open boundaries. Contrary to this expectation, we find that weak disorder changes the area-law scaling into a logarithmic scaling, while stronger disorder drives the system back into an area-law regime. At the critical point, the entanglement entropy exhibits a universal algebraic scaling under open boundary conditions. We further show that the log-law phase under open boundary conditions does not possess conformal invariance, and a transition from log-law to area-law entanglement also occurs under periodic boundary conditions.► BibTeX data@article{Li2026disorderinduced, doi = {10.22331/q-2026-08-07-2186}, url = {https://doi.org/10.22331/q-2026-08-07-2186}, title = {Disorder-{I}nduced {E}ntanglement {P}hase {T}ransitions in {N}on-{H}ermitian {S}ystems with {S}kin {E}ffects}, author = {Li, Kai and Liu, Ze-Chuan and Xu, Yong}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2186}, month = aug, year = {2026} }► References [1] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Nat. Phys. 14, 11 (2018). https://doi.org/10.1038/nphys4323 [2] Y. Xu, Front. Phys. 14, 43402 (2019). https://doi.org/10.1007/s11467-019-0896-1 [3] D.-W. 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This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractNon-Hermitian dynamics is ubiquitous in various physical systems. While recent study shows that such a dynamics leads to an area-law scaling of the entanglement entropy due to the non-Hermitian skin effects, it remains unclear how disorder changes the behavior of the entanglement entropy in a non-Hermitian system with skin effects. Here we study the dynamics of a many-body state of free fermions in the paradigmatic Hatano-Nelson model with open boundaries, and find that the area-law behavior of the entanglement entropy in the pristine Hatano-Nelson model develops into a logarithmic scaling for small disorder strength. As we further increase the disorder strength, the system reenters an area-law regime through an entanglement phase transition. At the critical point, the entanglement entropy exhibits a universal algebraic scaling. We further demonstrate the absence of a conformal invariance in the log-law regime by examining the subsystem entanglement entropy, the connected correlation function and the mutual information. Finally, we show the existence of disorder induced entanglement phase transitions in the Hatano-Nelson model with periodic boundaries.Featured image: (a) Entanglement phase diagram of the disordered Hatano-Nelson model under open boundary conditions, showing log-law and area-law regimes separated by a phase boundary with algebraic entanglement scaling. (b) Half-system entanglement entropy $S_{L/2}$ versus system size $L$ for different disorder strengths at $\gamma=-0.5$. At the critical point $W=3.35$, $S_{L/2}\propto L^{0.5}$.Popular summaryNon-Hermitian skin effects can inhibit entanglement growth, resulting in area-law entanglement in the absence of disorder. Disorder can induce Anderson localization, which also suppresses entanglement growth. Since both mechanisms suppress entanglement, one might expect the area-law behavior to persist as disorder is introduced. In this work, we study the dynamics of a half-filled many-body state in the disordered Hatano-Nelson model with open boundaries. Contrary to this expectation, we find that weak disorder changes the area-law scaling into a logarithmic scaling, while stronger disorder drives the system back into an area-law regime. At the critical point, the entanglement entropy exhibits a universal algebraic scaling under open boundary conditions. We further show that the log-law phase under open boundary conditions does not possess conformal invariance, and a transition from log-law to area-law entanglement also occurs under periodic boundary conditions.► BibTeX data@article{Li2026disorderinduced, doi = {10.22331/q-2026-08-07-2186}, url = {https://doi.org/10.22331/q-2026-08-07-2186}, title = {Disorder-{I}nduced {E}ntanglement {P}hase {T}ransitions in {N}on-{H}ermitian {S}ystems with {S}kin {E}ffects}, author = {Li, Kai and Liu, Ze-Chuan and Xu, Yong}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2186}, month = aug, year = {2026} }► References [1] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Nat. Phys. 14, 11 (2018). https://doi.org/10.1038/nphys4323 [2] Y. Xu, Front. Phys. 14, 43402 (2019). https://doi.org/10.1007/s11467-019-0896-1 [3] D.-W. Zhang, Y.-Q. Zhu, Y. X. Zhao, H. Yan, and S.-L. Zhu, Adv. Phys. 67, 253 (2018). https://doi.org/10.1080/00018732.2019.1594094 [4] Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69, 249 (2020). https://doi.org/10.1080/00018732.2021.1876991 [5] E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Rev. Mod. Phys. 93, 015005 (2021). https://doi.org/10.1103/RevModPhys.93.015005 [6] T. E. Lee, Phys. Rev. Lett. 116, 133903 (2016). https://doi.org/10.1103/PhysRevLett.116.133903 [7] Y. Xu, S.-T. Wang, and L.-M. Duan, Phys. Rev. Lett. 118, 045701 (2017). https://doi.org/10.1103/PhysRevLett.118.045701 [8] D. Leykam, K. Y. Bliokh, C. Huang, Y. D. Chong, and F. Nori, Phys. Rev. Lett. 118, 040401 (2017). https://doi.org/10.1103/PhysRevLett.118.040401 [9] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018). https://doi.org/10.1103/PhysRevLett.120.146402 [10] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. 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