Disorder-Induced Entanglement Phase Transitions in Non-Hermitian Systems with Skin Effects

Kai Li; Ze-Chuan Liu; Yong Xu

doi:10.22331/q-2026-08-07-2186

Disorder-Induced Entanglement Phase Transitions in Non-Hermitian Systems with Skin Effects

Kai Li¹, Ze-Chuan Liu¹, and Yong Xu^1,2

¹Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
²Hefei National Laboratory, Hefei 230088, PR China

Published:	2026-08-07, volume 10, page 2186
Editor:	Himadri Shekhar Dhar
Eprint:	arXiv:2305.12342v3
Doi:	https://doi.org/10.22331/q-2026-08-07-2186
Citation:	Quantum 10, 2186 (2026).

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Abstract

Non-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 summary

Non-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}
}

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