Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation

Based on conditional past–future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin–Meshkov–Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, wi...

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Main Authors:	Liping Han, Jian Zou, Hai Li, Bin Shao
Format:	Article
Language:	English
Published:	MDPI AG 2020-08-01
Series:	Entropy
Subjects:	non-Markovianity Lipkin–Meshkov–Glick (LMG) model conditional past–future (CPF) correlation
Online Access:	https://www.mdpi.com/1099-4300/22/8/895

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spelling	doaj-9f751e55da5b408ab8134f019388fe412020-11-25T03:19:33ZengMDPI AGEntropy1099-43002020-08-012289589510.3390/e22080895Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future CorrelationLiping Han0Jian Zou1Hai Li2Bin Shao3School of Physics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Physics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Information and Electronic Engineering, Shandong Technology and Business University, Yantai 264005, ChinaSchool of Physics, Beijing Institute of Technology, Beijing 100081, ChinaBased on conditional past–future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin–Meshkov–Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, with respect to a particular set of CPF measurement operators, can be zero, which means that in this case the non-Markovianity of the system could not be detected. Furthermore, the initial system–bath correlations only slightly influence the non-Markovianity of the system in our model. Significantly, it is also found that the dynamics of the system for LMG baths, initially in the ground states corresponding to the symmetric phase and symmetry broken phase, exhibit different properties, and the maximal value of the CPF at the critical point is the smallest, independent of the measurement operator, which means that the criticality can manifest itself by the CPF. Moreover, the effect of bath temperature on the quantum criticality of the CPF depends on the measurement operator.https://www.mdpi.com/1099-4300/22/8/895non-MarkovianityLipkin–Meshkov–Glick (LMG) modelconditional past–future (CPF) correlation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Liping Han Jian Zou Hai Li Bin Shao
spellingShingle	Liping Han Jian Zou Hai Li Bin Shao Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation Entropy non-Markovianity Lipkin–Meshkov–Glick (LMG) model conditional past–future (CPF) correlation
author_facet	Liping Han Jian Zou Hai Li Bin Shao
author_sort	Liping Han
title	Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation
title_short	Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation
title_full	Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation
title_fullStr	Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation
title_full_unstemmed	Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation
title_sort	non-markovianity of a central spin interacting with a lipkin–meshkov–glick bath via a conditional past–future correlation
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2020-08-01
description	Based on conditional past–future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin–Meshkov–Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, with respect to a particular set of CPF measurement operators, can be zero, which means that in this case the non-Markovianity of the system could not be detected. Furthermore, the initial system–bath correlations only slightly influence the non-Markovianity of the system in our model. Significantly, it is also found that the dynamics of the system for LMG baths, initially in the ground states corresponding to the symmetric phase and symmetry broken phase, exhibit different properties, and the maximal value of the CPF at the critical point is the smallest, independent of the measurement operator, which means that the criticality can manifest itself by the CPF. Moreover, the effect of bath temperature on the quantum criticality of the CPF depends on the measurement operator.
topic	non-Markovianity Lipkin–Meshkov–Glick (LMG) model conditional past–future (CPF) correlation
url	https://www.mdpi.com/1099-4300/22/8/895
work_keys_str_mv	AT lipinghan nonmarkovianityofacentralspininteractingwithalipkinmeshkovglickbathviaaconditionalpastfuturecorrelation AT jianzou nonmarkovianityofacentralspininteractingwithalipkinmeshkovglickbathviaaconditionalpastfuturecorrelation AT haili nonmarkovianityofacentralspininteractingwithalipkinmeshkovglickbathviaaconditionalpastfuturecorrelation AT binshao nonmarkovianityofacentralspininteractingwithalipkinmeshkovglickbathviaaconditionalpastfuturecorrelation
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Non-Markovianity of A Central Spin Interacting with a Lipkin–Meshkov–Glick Bath via a Conditional Past–Future Correlation

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