Decoupling the Magnetic Field Operator as an Independent Operator Class in Stochastic Series Expansion Quantum Monte Carlo

The Stochastic Series Expansion (SSE) quantum Monte Carlo method with loop updates is among the most powerful approaches for quantum spin and boson systems. In the standard formulation, the magnetic field term is routinely absorbed into the Heisenberg interactions---a strategy that has proven highly efficient across a wide range of field strengths. In this work, we propose a more general SSE framework in which the magnetic field operator is treated as an independent operator class, enabling it to participate in Monte Carlo updates on an equal footing with all other operators. Importantly, the field operator and other interaction operators can transform into one another during the update process. We demonstrate this algorithm using the two-dimensional antiferromagnetic Heisenberg model in a magnetic field as a concrete example. The simulation results agree with those of the conventional algorithm, confirming the correctness of the new formulation. A comparison of the integrated autocorrelation time shows that the new algorithm is competitive. This flexibility not only facilitates measurements of observables associated with operators but also offers potential computational advantages for a broader class of problems.