  The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically
samples the exact $N$-body density matrix for interacting electrons at finite
temperature. We introduce a simple modification to the interaction picture
DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one
inverse temperature point at a time, instead allowing for the sampling of a
temperature range within a single calculation thereby reducing the
computational cost. At the target inverse temperature, instead of ending the
simulation, we incorporate a change of picture away from the interaction
picture. The resulting equations of motion have piecewise functions and use the
interaction picture in the first phase of a simulation, followed by the
application of the Bloch equation once the target inverse temperature is
reached. We find that the performance of this method is similar to or better
than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
