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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Main Authors: Yue-Mei Sun, Xinyu Wang, Liang-Jun Zhai
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Entropy
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Online Access:https://www.mdpi.com/1099-4300/27/2/170
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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.
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institution DOAJ
issn 1099-4300
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publishDate 2025-02-01
publisher MDPI AG
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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