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Journal of Sichuan University

The effect of algebraic structure breaking of Hamiltonian on geometric phase

Qing-Wu Wang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Using algebraic dynamics and matrix diagnization,the geometric phase of a non-symmetry 3-particle spin chain has been calculated.The dependence of the geometric phase of this system on the algebraic structure of Hamiltonian is studied.It is found that when the algebraic structure of Hamiltonian is broken,a drastic change in the structure of the geometric phase takes place.

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Geometric Phase of the 3-particle Spin Chain

Song Yuan-jun, Shun-Jin Wang

Using algebraic dynamics, the geometric phase of a 3-particle spin chain has been calculated. The dependence of the geometric phase of this system on the symmetry of Hamiltonian is investigated. It is found that when the symmetry of Hamiltonian is broken, a drastic change in the structure of the geometric phase takes place.

Journal of Sichuan University•Jan 1, 2005•0 citations

Homotrinuclear Spin Cluster with Orbital Degeneracy in a Magnetic Field: Algebraic Dynamic Studies of the Geometric Phase

Ji-Wen Chenga, Qin-Sheng Zhua, Xiao-Yu Kuanga +2 more

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.

•Jan 1, 2008•0 citations

Homotrinuclear spin cluster with orbital degeneracy in a magnetic field: Algebraic dynamic studies of the geometric phase

J. W. Chen, Qin‐Feng Zhu, Kuang Xiao-Yu +2 more

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.

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Geometric Phase of a Heisenberg-chain

Xiaoyan Deng

Objective The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain,in order to find out how the coulping strengths between spins influence the geometric phase of this system.Method An interacting anisotropic 3-spin 1/2 system,which is driven by a rotating magnetic field,is considered.The system has a su(2) algebraic structure.By an unitary gauge transformation,this nonautonomous system becomes an autonomous system.The Schrodinger equation of the autonomous system is solved.By virtue of the inverse transformation of the original gauge transformation,the exact analytical solution to the time dependent Schrodinger equation is obtained in total spin 1/2 subspace.Resutlt The geometric phases in this subspace are calculated.Conclusion The result shows that(i)Coulping strengths don't influence the geometric phases of this system;(ii) The geometric phases of the system is the same as that of one spin 1/2 system in a rotating magnetic field.

Journal of Hebei North University•Jan 1, 2008•0 citations

Homotrinuclear Spin Cluster with Orbital Degeneracy in a Magnetic Field: Algebraic Dynamic Studies of the Geometric Phase January 25, 2008

Ji-Wen Cheng, Qinsheng Zhu, Kuang Xiao-Yu +2 more

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.

Zeitschrift für Naturforschung A•Aug 1, 2008•0 citations

Quantifying algebraic asymmetry of Hamiltonian systems

Hui-Hui Qin, Shao-Ming Fei, Chang-Pu Sun

Abstract Symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra and its q -deformation. The asymmetry of the q -deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.

arXiv:2001.02410•Journal of Physics A Mathematical and Theoretical•Nov 25, 2019•1 citation
Using algebraic dynamics and matrix diagnization,the geometric phase of a non-symmetry 3-particle spin chain has been calculated.The dependence of the geometric phase of this system on the algebraic structure of Hamiltonian is studied.It is found that when the algebraic structure of Hamiltonian is broken,a drastic change in the structure of the geometric phase takes place.
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.
Objective The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain,in order to find out how the coulping strengths between spins influence the geometric phase of this system.Method An interacting anisotropic 3-spin 1/2 system,which is driven by a rotating magnetic field,is considered.The system has a su(2) algebraic structure.By an unitary gauge transformation,this nonautonomous system becomes an autonomous system.The Schrodinger equation of the autonomous system is solved.By virtue of the inverse transformation of the original gauge transformation,the exact analytical solution to the time dependent Schrodinger equation is obtained in total spin 1/2 subspace.Resutlt The geometric phases in this subspace are calculated.Conclusion The result shows that(i)Coulping strengths don't influence the geometric phases of this system;(ii) The geometric phases of the system is the same as that of one spin 1/2 system in a rotating magnetic field.
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.
Abstract Symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra and its q -deformation. The asymmetry of the q -deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.