Recognizing critical lines via entanglement in non-Hermitian systems

Year: 2026

Authors: Das Agarwal K., Konar T.K., Lakkaraju L.G.C., Sen A.

Autors Affiliation: A CI Homi Bhabha Natl Inst, Harish Chandra Res Inst, Chhatnag Rd, Allahabad 211019, India; Univ Trento, Pitaevskii BEC Ctr, CNR, INO, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Trento Inst Fundamental Phys & Applicat, INFN, Via Sommar 14, I-38123 Trento, Italy.

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-ShekhtmanEntin-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- 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.

Journal/Review: PHYSICAL REVIEW A

Volume: 113 (2)      Pages from: 22201-1  to: 22201-14

More Information: We acknowledge the support from Interdisciplinary Cyber Physical Systems (ICPS) program of the Department of Science and Technology (DST), India, Grant No.: DST/ICPS/QuST/Theme-1/2019/23. We acknowledge the use of QIClib, a modern C++ library for general purpose quantum information processing and quantum computing [105] and cluster computing facility at Harish-Chandra Research Institute. L.G.C.L. is funded by the European Uni on. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the granting authority can be held responsible for them. This project has been funded by the Caritro Foundation. This work was supported by the Provincia Autonoma di Trento, and Q@TN, the joint lab between the University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR- National Research Council, Italy.
KeyWords: Statistical-mechanics; Xy-model; Separability
DOI: 10.1103/b5sd-fn57