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Chinese Physics Letters

Berry Phase in an Entangled Spin Cluster with Five Particles

Xiao-Bo Yan

Published Jul 26, 2007• 1 citation
Publisher

Abstract

The geometric phase, in particular the Berry phase, in an entangled state of five spin-1/2 particles is studied. A time-dependent magnetic field is applied to control the time evolution of the cluster. Using the method of algebraic dynamics, we calculate the non-adiabatic geometric phase or Berry phase and the degeneracy energy levels when the magnetic rotates around Z axis. Based on the exact analytical solutions, we show how the Berry phase of the entangled state of this cluster depends on the external magnetic field parameters ω (the angular velocity of the rotating magnetic field) and θ (the angle between the magnetic field and Z axis).

DOI
10.1088/0256-307x/24/8/005

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Based on the homotrinuclear spin cluster having SU(2)⊗SU(2) symmetry with twofold orbital degeneracy τ = 1/2) and the SU(2) algebraic structures of both ŝ and τ subspaces in the external magnetic field, we calculate exactly the non-adiabatic energy levels and the cyclic and non-cyclic non-adiabatic geometric phase of the homotrinuclear spin cluster by making use of the method of algebraic dynamics. The solution will show that the Berry phase is much influenced by the parameters N = γs/γτ (γs and γτ are the magnetic momentums of ŝ and τ subspaces, respectively) in addition to ω/Ω in a rotating magnetic field. The change of the Berry phase in the basis state of the system is demonstrated from the changing diagram.
Based on he homotrinuclear spin cluster having SU(2)circle times SU(2) symmetry With twofold orbital degeneracy tau = 1/2) and the SU(2) algebraic structures of both (s) over cap and (tau) over cap subspaces in the external magnetic field. We calculate exactly the non-adiabatic energy levels and the cyclic and non-cyclic non-adiabatic geometric phase of the homotrinuclear spin cluster by making use of the method of algebraic dynamics. The solution Will show that the Berry phase is much influenced by the parameters N = gamma(s)/gamma(tau) (gamma(s) and gamma(tau) are the magnetic momentums of (s) over cap and (tau) over cap subspaces, respectively) in addition to omega/Omega in a rotating magnetic field. The change of the Berry phase in the basis state of the system is demonstrated from the changing diagram.
Using the method of dynamical algebras, the solution of a homotriparticle linear spin cluster (each particle with S=1∕2S=1∕2S=1∕2) in a rotating magnetic field is obtained. We derive degeneracy energy levels and each level's Berry phase of this system. The Berry phase as a function of $\ensuremath{\omega}$ and $\ensuremath{\theta}$ has been determined by using the relation between the Berry phase and the angular velocity $\ensuremath{\omega}$ of the rotating magnetic field as well as the angle $\ensuremath{\theta}$ between the magnetic field and ZZZ axis. We obtain the changing diagram of the Berry phase of the basis state.
Based on the homotrinuclear spin cluster having SU(2)⊗SU(2) symmetry with twofold orbital degeneracy τ = 1/2) and the SU(2) algebraic structures of both ŝ and τˆ subspaces in the external magnetic field, we calculate exactly the non-adiabatic energy levels and the cyclic and non-cyclic non-adiabatic geometric phase of the homotrinuclear spin cluster by making use of the method of algebraic dynamics. The solution will show that the Berry phase is much influenced by the parameters N =γ s /γ τ (γ s and γ τ are the magnetic momentums of ŝ and τ̂ subspaces, respectively) in addition to ω/Ω in a rotating magnetic field. The change of the Berry phase in the basis state of the system is demonstrated from the changing diagram.
The entanglement dependence of Berry's geometric phase is studied in the case of two spin-1/2 particles with a spin-spin interaction.Berry's phases for two spin-1/2 entanglement particles in the presence of spin-spin interaction and noninteraction are calculated,respectively.The expression of calculating geometric phase,when entanglement vanishes,is obtained.Moreover,the geometric phase is discussed when only one of the two particles is affected by the external magnetic field.It is shown that its geometric phase is not equal to that of single particle which is acted by the external magnetic field,and the result is related toαthat affect the strength of entanglement. A general entanglement-dependence geometric phase is formulated.