We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g. the adiabatic limits of the geometric phases, being 2π and π in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g. the adiabatic limits of the geometric phases, being 2π and π in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.

Mar 24, 20163 citations

Mixed-state geometric phases of coherent and squeezed spin states

Xin Wang, Jia-Chen Tang, Xu-Yang Hou +2 more

Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j=3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j=1$ one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j=1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.Two mixed-state geometric phases, known as the Uhlmann phase and interferometric geometric phase (IGP), of spin coherent states (CSSs) and spin squeezed states (SSSs) are analyzed. Exact solutions and numerical results of selected examples are presented. For the $j=3/2$ CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the $j=1$ one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the $j=1$ two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.

arXiv:2502.07268Physical review. B./Physical review. BJun 27, 20252 citations

Dynamical topological quantum phase transitions in a finite-size spin system

Shaoying Yin, Hongchun Sun, Jin‐Liang Guo +2 more

Chinese Journal of PhysicsNov 21, 20251 citation

Topological Quantum Phase Transition in One-dimensional Spin Chain

Hong‐Chen Jiang, Jiadong Zang, Zheng-Yu Weng +1 more

Bulletin of the American Physical SocietyMar 17, 20100 citations

Topological transitions of the generalized Pancharatnam-Berry phase

Manuel F. Ferrer-Garcia, Kyrylo Snizhko, Alessio D’Errico +3 more

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.

Science AdvancesNov 24, 202313 citations

j=3/2

CSS, the Uhlmann phase exhibits finite-temperature topological phase transitions characterized by abrupt jumps. The IGP for the same state similarly shows discontinuous jumps as the temperature varies. In the case of the

j=1

one-axis SSS, both the Uhlmann phase and IGP display discrete finite-temperature jumps. By contrast, the

j=1

two-axis SSS shows no such transitions because the Uhlmann phase and IGP both vary smoothly with temperature. We also briefly discuss potential realizations and simulations related to these phenomena in spin systems.