Solution to Sign Problems in Models of Interacting Fermions and Quantum Spins

We show that solutions to fermion sign problems that are found in the formulation where the path integral is expanded in powers of the interaction in continuous time can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the world-line representation of quantum spins. Combining this idea with meron-cluster methods, we are able to further extend the class of models that are solvable. We demonstrate these solutions to sign problems by considering several examples of strongly correlated systems that contain the physics of semimetals, insulators, superfluidity, and antiferromagnetism.