Critical Relaxation in the Quantum Yang–Lee Edge Singularity
We study the relaxation dynamics near the critical points of the Yang–Lee edge singularities (YLESs) in the quantum Ising chain in an imaginary longitudinal field with a polarized initial state. We find that scaling behaviors are manifested in the relaxation process after a non-universal transient t...
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2025-02-01
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| author | Yue-Mei Sun Xinyu Wang Liang-Jun Zhai |
| author_facet | Yue-Mei Sun Xinyu Wang Liang-Jun Zhai |
| author_sort | Yue-Mei Sun |
| collection | DOAJ |
| description | We study the relaxation dynamics near the critical points of the Yang–Lee edge singularities (YLESs) in the quantum Ising chain in an imaginary longitudinal field with a polarized initial state. We find that scaling behaviors are manifested in the relaxation process after a non-universal transient time. We show that for the paramagnetic Hamiltonian, the magnetization oscillates periodically with the period being inversely proportional to the gap between the lowest energy level; for the ferromagnetic Hamiltonian, the magnetization decays to a saturated value; while for the critical Hamiltonian, the magnetization increases linearly. A scaling theory is developed to describe these scaling properties. In this theory, we show that for a small- and medium-sized system, the scaling behavior is described by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional YLES. |
| format | Article |
| id | doaj-art-2d26a2fa170c46189b2fb2f56ac53213 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-2d26a2fa170c46189b2fb2f56ac532132025-08-20T03:12:11ZengMDPI AGEntropy1099-43002025-02-0127217010.3390/e27020170Critical Relaxation in the Quantum Yang–Lee Edge SingularityYue-Mei Sun0Xinyu Wang1Liang-Jun Zhai2The School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, ChinaThe School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, ChinaThe School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, ChinaWe study the relaxation dynamics near the critical points of the Yang–Lee edge singularities (YLESs) in the quantum Ising chain in an imaginary longitudinal field with a polarized initial state. We find that scaling behaviors are manifested in the relaxation process after a non-universal transient time. We show that for the paramagnetic Hamiltonian, the magnetization oscillates periodically with the period being inversely proportional to the gap between the lowest energy level; for the ferromagnetic Hamiltonian, the magnetization decays to a saturated value; while for the critical Hamiltonian, the magnetization increases linearly. A scaling theory is developed to describe these scaling properties. In this theory, we show that for a small- and medium-sized system, the scaling behavior is described by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional YLES.https://www.mdpi.com/1099-4300/27/2/170critical relaxationYang–Lee edge singularityparity-time symmetry breaking phase transition |
| spellingShingle | Yue-Mei Sun Xinyu Wang Liang-Jun Zhai Critical Relaxation in the Quantum Yang–Lee Edge Singularity Entropy critical relaxation Yang–Lee edge singularity parity-time symmetry breaking phase transition |
| title | Critical Relaxation in the Quantum Yang–Lee Edge Singularity |
| title_full | Critical Relaxation in the Quantum Yang–Lee Edge Singularity |
| title_fullStr | Critical Relaxation in the Quantum Yang–Lee Edge Singularity |
| title_full_unstemmed | Critical Relaxation in the Quantum Yang–Lee Edge Singularity |
| title_short | Critical Relaxation in the Quantum Yang–Lee Edge Singularity |
| title_sort | critical relaxation in the quantum yang lee edge singularity |
| topic | critical relaxation Yang–Lee edge singularity parity-time symmetry breaking phase transition |
| url | https://www.mdpi.com/1099-4300/27/2/170 |
| work_keys_str_mv | AT yuemeisun criticalrelaxationinthequantumyangleeedgesingularity AT xinyuwang criticalrelaxationinthequantumyangleeedgesingularity AT liangjunzhai criticalrelaxationinthequantumyangleeedgesingularity |