Preserving positivity in density-explicit field-theoretic simulations

Field-theoretic simulations are numerical methods for polymer field theory, which include fluctuation corrections beyond the mean-field level, successfully capturing various mesoscopic phenomena. Most field-theoretic simulations of polymeric fluids use the auxiliary field (AF) theory framework, which employs Hubbard-Stratonovich transformations for the particle-to-field conversion. Nonetheless, the Hubbard-Stratonovich transformation imposes significant limitations on the functional form of the non-bonded potentials. Removing this restriction on the non-bonded potentials will enable studies of a wide range of systems that require multi-body or more complex potentials. An alternative representation is the hybrid density-explicit auxiliary field theory (DE-AF), which retains both a density field and a conjugate auxiliary field for each species. While the DE-AF representation is not new, density-explicit field-theoretic simulations have yet to be developed. A major challenge is preserving the real and non-negative nature of the density field during stochastic evolution. To address this, we introduce positivity-preserving schemes that enable the first stable and efficient density-explicit field-theoretic simulations (DE-AF FTS). By applying the new method to a simple fluid, we find thermodynamically correct results at high densities, but the algorithm fails in the dilute regime. Nonetheless, DE-AF FTS is shown to be broadly applicable to dense fluid systems including a simple fluid with a three-body non-bonded potential, a homopolymer solution, and a diblock copolymer melt.