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 spin systems subject to magnetic fields that can be time dependent and can accommodate the presence of Heisenberg exchange interactions between the spins. This is done by deriving an effective magnetic field from the quantum partition function of the system to use in classical atomistic spin dynamics simulations and generalizes the formalism presented in our previous work [Phys. Rev. Res. 5, 043075 (2023)]. In special cases where the effective field can be computed exactly, we compare our results with exact/numerical diagonalization methods for both ferromagnetic and antiferromagnetic coupling. We show that our method works well across a large temperature range and can reproduce quantum expectation values for antiferromagnetic coupling, which is usually not possible with classical models.