Recognizing critical lines via entanglement in non-Hermitian systems

Abstract: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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2305.08374 [quant-ph]

(or arXiv:2305.08374v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2305.08374 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 113, 022201 (2026)

https://doi.org/10.1103/b5sd-fn57 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.