A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians

We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a previously developed PMR-QMC method for spin-1/2 Hamiltonians [Phys. Rev. Research 6, 013281 (2024)]. Because it does not rely on a local bond decomposition, the method applies equally well to models with arbitrary connectivities, long-range and multi-spin interactions, and its closed-walk formulation allows a natural analysis of sign-problem conditions in terms of cycle weights. To demonstrate its applicability and versatility, we apply our method to spin-1 and spin-3/2 quantum Heisenberg models on the square lattice, as well as to randomly generated high-spin Hamiltonians. Additionally, we show how the approach naturally extends to general Hamiltonians involving mixtures of particle species, including bosons and fermions. We have made our program code freely accessible on GitHub.