  We introduce a novel simple algorithm for thermostatting path integral
molecular dynamics (PIMD) with the Langevin equation. The staging
transformation of path integral beads is employed for demonstration. The
optimum friction coefficients for the staging modes in the free particle limit
are used for all systems. In comparison to the path integral Langevin equation
(PILE) thermostat, the new algorithm exploits a different order of splitting
for the phase space propagator associated to the Langevin equation. While the
error analysis is made for both algorithms, they are also employed in the PIMD
simulations of three realistic systems (the H2O molecule, liquid para-hydrogen,
and liquid water) for comparison. It is shown that the new thermostat increases
the time interval of PIMD by a factor of 4~6 or more for achieving the same
accuracy. In addition, supplemental material shows the error analysis made for
the algorithms when the normal-mode transformation of path integral beads is
used.
