Path integral spin dynamics with exchange and external field

In this work, we propose a path integral-inspired formalism for computing the quantum thermal expectation values of spins, when subject to magnetic fields that can be time-dependent and can accommodate the presence of Heisenberg exchange interactions between the spins. This generalises the formalism presented in our previous work [Phys. Rev. Research 5, 043075 (2023)] and paves the way towards the realisation of large-scale atomistic simulations, for which this method should reveal its true efficiency gains, when compared to exact quantum methods. We compare our results with exact/numerical diagonalisation methods, where possible, to confirm the range of accuracy of our model.