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Geometric phase and quantum phase transition in the Lipkin–Meshkov–Glick model

H. T. Cui, Kai Li, X. X. Yi

arXiv:quant-ph/0608203Physics Letters AAug 25, 200627 citations

Geometrical Phase, Generalized Quasienergy and Floquet Operator as Invariants

Vladimir I. Man’ko

Springer eBooksJan 1, 19933 citations

Aharonov—Anandan Phases in Lipkin—Meskov—Glick Model

Da-Bao Yang, Jing‐Ling Chen

In the system of several interacting spins, geometric phases have been researched intensively. However, the studies are mainly focused on the adiabatic case (Berry phase), so it is necessary for us to study the non-adiabatic counterpart (Aharonov and Anandan phase). In this paper, we analyze both the non-degenerate and degenerate geometric phase of Lipkin—Meskov—Glick type model, which has many application in Bose—Einstein condensates and entanglement theory. Furthermore, in order to calculate degenerate geometric phases, the Floquet theorem and decomposition of operator are generalized. And the general formula is achieved.In the system of several interacting spins, geometric phases have been researched intensively. However, the studies are mainly focused on the adiabatic case (Berry phase), so it is necessary for us to study the non-adiabatic counterpart (Aharonov and Anandan phase). In this paper, we analyze both the non-degenerate and degenerate geometric phase of Lipkin—Meskov—Glick type model, which has many application in Bose—Einstein condensates and entanglement theory. Furthermore, in order to calculate degenerate geometric phases, the Floquet theorem and decomposition of operator are generalized. And the general formula is achieved.

arXiv:1009.0411Communications in Theoretical PhysicsAug 1, 20112 citations

Aharonov-Anandan Phases in Lipkin-Meskov-Glick Model

Yang Da Bao, 陈景灵

In the system of several interacting spins,geometric phases have been researched intensively.However,the studies are mainly focused on the adiabatic case (Berry phase),so it is necessary for us to study the non-adiabaticcounterpart (Aharonov and Anandan phase).In this paper,we analyze both the non-degenerate and degenerate geometricphase of Lipkin-Meskov-Glick type model,which has many application in Bose-Einstein condensates and entanglementtheory.Furthermore,in order to calculate degenerate geometric phases,the Floquet theorem and decomposition ofoperator are generalized.And the general formula is achieved.In the system of several interacting spins,geometric phases have been researched intensively.However,the studies are mainly focused on the adiabatic case (Berry phase),so it is necessary for us to study the non-adiabaticcounterpart (Aharonov and Anandan phase).In this paper,we analyze both the non-degenerate and degenerate geometricphase of Lipkin-Meskov-Glick type model,which has many application in Bose-Einstein condensates and entanglementtheory.Furthermore,in order to calculate degenerate geometric phases,the Floquet theorem and decomposition ofoperator are generalized.And the general formula is achieved.

理论物理通讯：英文版Jan 1, 20110 citations

Equivalence of Many-Mode Floquet Theory to Floquet Theory

A. N. Poertner, J. D. D. Martin

Bulletin of the American Physical SocietyMay 30, 20190 citations

A Non-Abelian Geometric Phase for Spin Systems

Bharath Hebbe Madhusudhana, Matthew Boguslawski, Maryrose Barrios +1 more

Bulletin of the American Physical SocietyMar 16, 20170 citations

Generalization of Floquet theorom and decompostion of operator mothods to the non-abelian Geometric phase and application to Lipkin-Meshkov-Glick model

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Generalization of Floquet theorom and decompostion of operator mothods to the non-abelian Geometric phase and application to Lipkin-Meshkov-Glick model

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