Applying Permutation Matrix Representation Quantum Monte Carlo to higher-spin systems and fermionic systems

We present a universal, parameter-free quantum Monte Carlo algorithm designed to simulate arbitrary high-spin (greater than spin-1/2) Hamiltonians. This method is based on the recently introduced Permutation Matrix Representation Quantum Monte Carlo (PMR-QMC) framework, which allows for the general treatment of entire classes of Hamiltonians, eliminating the need for system-specific update rules [1, 2].

Additionally, we introduce a PMR-QMC algorithm for simulating arbitrary fermionic systems, such as the Fermi-Hubbard model on arbitrary graphs and electronic structure problems. We also examine the sign problem.

To demonstrate the applicability and versatility of our approach, we present simulation results for the spin-1 quantum Heisenberg model, Fermi-Hubbard models on two-dimensional lattices, and electronic structure problems.