Fast-forward adiabatic quantum dynamics of XY spin model on three spin system

We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity function together with the original Hamiltonian give fast-forward driving for adiabatic states. We apply our method to XY spin model by considering three spin systems on the Kagome lattice. In this model, we obtained the XY pair-wise exchange interaction of nearest neighbors and next-nearest neighbors should be added to the original Hamiltonian as a driving interaction to accelerate the adiabatic motion. This pair-wise driving interaction in the fast-forward scheme guarantees the complete fidelity of accelerated states.

Automated summary

We discussed the use of the fast-forward method proposed by Masuda and Nakamura to accelerate the adiabatic quantum dynamics of the XY spin model. The accelerated scheme involves adding a driving Hamiltonian to the original Hamiltonian and increasing the speed with a large time-scaling factor and an adiabatic parameter. By assuming the driving Hamiltonian consists of pair-wise exchange interaction and a magnetic field, the fast-forward driving is achieved for adiabatic states. We applied this method to the XY spin model on the Kagome lattice and found that adding the XY pair-wise exchange interaction of nearest and next-nearest neighbors as a driving interaction accelerates the adiabatic motion, ensuring complete fidelity of accelerated states.