Improved methods for path integral Monte Carlo integration in fermionic systems

We generalize the discretized Feynman path integral expansion by replacing the path through pure states with a path through idempotent density matrices. The transformed expression converges to the ordinary path integral, but is computationally more flexible than the ordinary form. By introducing a particular choice of these idempotent density matrices, based on rotational averaging around the two-particle center of mass, we greatly reduce the sign problem for systems of two fermions in three dimensions. In the ordinary path integral Monte Carlo approach, low temperature simulation of fermions is inefficient as the integral decays exponentially faster than the integrand (and its variance) as the temperature decreases. The new rotationally averaged algorithm dramatically retards this relative decay. Fermionic simulations of the model system of Kestner and Sinanoglu, and of the harmonic oscillator, demonstrate this improvement, as integrals calculated at temperatures much lower than the singlet–triplet splitting display negligible decay of the desired averages relative to the partition function of the modified path ensemble.