We consider a charged quantum particle living in the Lobachevsky plane and interacting with a homogeneous magnetic field perpendicular to the plane and a point interaction which is transported adiabatically along a closed loop C in the plane. We show that the bound-state eigenfunction acquires at that the Berry phase equal to 2 times the number of the flux quanta through the area encircled by C. 1 Introduction The phenomena arising from a geometric phase called Berry phase [Ber] have been put in evidence in many quantum mechanical systems. Recently such a "Berry phase effect" has been observed in some magnetic systems [LSG, MHK]. Moreover, it was shown that the geometric phase can emerge even in a time-independent homogeneous magnetic field when a potential 1 well trapping a two-dimensional particle is transported along a closed loop. An example in which the potential is of zero range is worked out in [EG], where a formula was proved showing that in the absence of an additional conf...We consider a charged quantum particle living in the Lobachevsky plane and interacting with a homogeneous magnetic field perpendicular to the plane and a point interaction which is transported adiabatically along a closed loop C in the plane. We show that the bound-state eigenfunction acquires at that the Berry phase equal to 2 times the number of the flux quanta through the area encircled by C. 1 Introduction The phenomena arising from a geometric phase called Berry phase [Ber] have been put in evidence in many quantum mechanical systems. Recently such a "Berry phase effect" has been observed in some magnetic systems [LSG, MHK]. Moreover, it was shown that the geometric phase can emerge even in a time-independent homogeneous magnetic field when a potential 1 well trapping a two-dimensional particle is transported along a closed loop. An example in which the potential is of zero range is worked out in [EG], where a formula was proved showing that in the absence of an additional conf...

Jan 1, 20007 citations

Berry’s phase under the Dzyaloshinskii-Moriya interaction

M. K. Kwan, Zeynep Nilhan Gürkan, L. C. Kwek

In this paper, we study the Dzyaloshinskii-Moriya (DM) anisotropic $XX$ spin-chain model in the presence of an external homogeneous magnetic field. We found that the Berry phase of the system varies interestingly with small and large amounts of DM interaction and the magnetic field. In addition, we also considered the concurrence (i.e., the amount of entanglement) of the system, and the relationship between the concurrence and the Berry phase. Finally, we calculate the Berry phase of thermal states and verify that the results are consistent with that of the pure states.In this paper, we study the Dzyaloshinskii-Moriya (DM) anisotropic $XX$ spin-chain model in the presence of an external homogeneous magnetic field. We found that the Berry phase of the system varies interestingly with small and large amounts of DM interaction and the magnetic field. In addition, we also considered the concurrence (i.e., the amount of entanglement) of the system, and the relationship between the concurrence and the Berry phase. Finally, we calculate the Berry phase of thermal states and verify that the results are consistent with that of the pure states.

Physical Review AJun 9, 200813 citations

Berry phase in magnetic systems with point perturbations

Pavel Exner, Vladimir A. Geyler

arXiv:quant-ph/9911060Journal of Geometry and PhysicsNov 1, 20008 citations

In this paper, we study the Dzyaloshinskii-Moriya (DM) anisotropic

XX

spin-chain model in the presence of an external homogeneous magnetic field. We found that the Berry phase of the system varies interestingly with small and large amounts of DM interaction and the magnetic field. In addition, we also considered the concurrence (i.e., the amount of entanglement) of the system, and the relationship between the concurrence and the Berry phase. Finally, we calculate the Berry phase of thermal states and verify that the results are consistent with that of the pure states.