  The Stochastic Series Expansion (SSE) quantum Monte Carlo method with
directed loops is very efficient for spin and boson systems. The Heisenberg
mode l and its generalizations, such as the $JQ_2$ model, are extensively
simulated via this method. When introducing magnetic field in these models, the
SSE method always combines the field with the diagonal part of the Heisenberg
interactions (${S_i}^z{S_j}^z$) and take them as the new diagonal operators. In
general, this treatment is reasonable. However, when studying Hamiltonians
which have other interactions or even don't contain the Heisenberg interactio
ns, this general treatment will not be efficient or even not work. We suggest
that when doing directed-loop simulations, the magnetic field can be put in to
other interactions. This new treatment, in some cases, improves the simulation
efficiency. Using the $JQ_2$ model with magnetic field as an example, w e here
demonstrate this new SSE method. Such new treatment significantly improves the
efficiency when the $Q_2$ interactions are large. The autocorrelati ons are
reduced a lot compared to the previous approach. In addition, we argue that we
can divide the magnetic field into two parts and combine them with both the $J$
and $Q$ operators respectively. This treatment also improves the simulation
efficiency. The underlying mechanism is that these two new SSE methods can
utilize the main part or even all part of operators in operator products to do
the directe d-loop updates. Such idea can also be applied to other models with
magnetic field and it will speed up the simulations.
