  A quantum Monte Carlo method combining update of the loop algorithm with the
global flip of the world line is proposed as an efficient method to study the
magnetization process in an external field, which has been difficult because of
inefficiency of the update of the total magnetization. The method is
demonstrated in the one dimensional antiferromagnetic Heisenberg model and the
trimer model. We attempted various other Monte Carlo algorithms to study
systems in the external field and compared their efficiency.
