{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:45:00Z","timestamp":1760240700719,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T00:00:00Z","timestamp":1566777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11704161 and  11547142"],"award-info":[{"award-number":["11704161 and  11547142"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Province of China","award":["BK20170309"],"award-info":[{"award-number":["BK20170309"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.<\/jats:p>","DOI":"10.3390\/e21090836","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T10:54:53Z","timestamp":1566816893000},"page":"836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Scaling of the Berry Phase in the Yang-Lee Edge Singularity"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4483-689X","authenticated-orcid":false,"given":"Liang-Jun","family":"Zhai","sequence":"first","affiliation":[{"name":"The School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huai-Yu","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Physics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang-Yao","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information &amp; State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,26]]},"reference":[{"key":"ref_1","first-page":"45","article-title":"Quantal Phase Factors Accompanying Adiabatic Changes","volume":"329","author":"Berry","year":"1984","journal-title":"Proc. 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