  Imaginary-time path integral (PI) is a rigorous quantum mechanical tool to
compute static properties. However, the stiff nature of the internal PI modes
poses a sampling challenge. This is commonly tackled using staging coordinates,
in which the free particle (FP) contribution of the PI action is diagonalized.
We introduce novel and simple staging coordinates that diagonalize the entire
action of the harmonic oscillator (HO), rendering it efficiently applicable to
systems with a harmonic character, such as quantum oscillators and crystals.
Unlike FP staging, the HO staging provides a unique treatment of the centroid
mode. We provide implementation schemes for PIMC and PIMD simulations. Sampling
efficiency is assessed in terms of precision and accuracy of estimating the
energy and heat capacity of a 1D HO, along with an anharmonic oscillator (AO)
to investigate anharmonic effects. In PIMC, the HO coordinates propose
collective moves that perfectly sample the HO contribution, then (for AO) the
residual anharmonic term is sampled using Metropolis method. This results in a
high acceptance rate and, hence, high precision, in comparison to the FP
staging. In PIMD, the HO coordinates naturally prescribe definitions for the
fictitious masses, yielding equal frequencies of all modes when applied to the
HO model. This allows for a substantially larger time step sizes relative to
standard staging, without affecting accuracy. For completeness, we also present
results using normal mode (NM) coordinates, based on both HO and FP models.
While staging and NM coordinates show similar performance, staging is
computationally cheaper due to its linear, rather than quadratic, scaling with
system size. The simplicity and the enhanced sampling gained by the HO
coordinates open avenues for efficient estimation of nuclear quantum effects in
more complex systems, such as molecular bonds and quantum crystals.
