Qualitatively different decaying behaviors of the quantum Loschmidt echo in the two phases of the LMG model

Wang Ping; Qian Wang; Yinbiao Yang; Wen-ge Wang

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Qualitatively different decaying behaviors of the quantum Loschmidt echo in the two phases of the LMG model

Wang Ping 1,Qian Wang 2,Yinbiao Yang 2,Wen-ge Wang 2 *

1.Department of Modern Physics, University of Science and Technology of China, Hefei 230026；Hunan Institute of Technology of China, HengYang 421165；Beijing Computational Science Research Center,Beijing 100084

2.Department of Modern Physics,University of Science and Technology of China, Hefei 230026

*Correspondence author

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Funding: Natural Science Foundation of China （No.11275179 and 10975123）, National Key Basic Research Program of China （No.2013CB921800）, Specialized Research Fund for the Doctoral Program of Higher Education of China（No.SRFDP）

Opened online:12 December 2013

Accepted by: none

Citation: Wang Ping,Qian Wang,Yinbiao Yang.Qualitatively different decaying behaviors of the quantum Loschmidt echo in the two phases of the LMG model[OL]. [12 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4573088

A unified expression of the quantum Loschmidt echo (LE) in the vicinity of the quantum phase transition in the Lipkin-Meshkov-Glick model is derived, which is valid both in the symmetric phase and in the broken phase. The LE shows qualitatively different decaying behaviors in the two phases, in particular, in the broken phase, it has a decay rate that diverges in the thermodynamic limit. In contrast to many-body systems, in which the LE also shows divergent decay rates in the thermodynamic limit due to the so-called orthogonality catastrophe, the considered motion in this model has a classical counterpart with one degree of freedom only.

Keywords:Quantum phase transition, Lipkin-Meshkov-Glick (LMG) model, Loschmidt echo(LE), Holstein-Primakoff transformation, decaying behaviors, decay rate

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