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

TL;DR

This paper presents a method to accelerate adiabatic quantum dynamics in XY spin models using a fast-forward approach, enabling quicker state evolution with high fidelity in three-spin Kagome lattice systems.

Contribution

The paper introduces a novel fast-forward scheme for adiabatic quantum dynamics in XY spin models, incorporating specific driving Hamiltonians for three-spin systems on Kagome lattices.

Findings

Accelerated adiabatic dynamics achieve high fidelity.

Pair-wise exchange interactions are essential for acceleration.

Method successfully shortens evolution time in three-spin systems.

Abstract

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.