Quantum simulations of realistic systems by auxiliary fields

Abstract

To treat interacting quantum systems, it is often crucial to have accurate calculations beyond the mean-field level. Many-body simulations based on field-theoretical approaches are a promising tool for this purpose and are applied in several sub-fields of physics, in closely related forms. An major difficulty is the sign or phase problem, which causes the Monte Carlo variance to increase exponentially with system size. We address this issue in the context of auxiliary-field simulations of realistic electronic systems in condensed matter physics. We show how to use importance sampling of the complex fields to control the phase problem. An approximate approach is formulated with a trial determinant to constrain the paths in field space and completely eliminate the growth of the noise. For ab initio electronic structure calculations, this gives a many-body approach in the form of a “coherent” superposition of mean-field calculations, allowing direct incorporation of state-of-the-art technology from the latter (non-local pseudopotentials; high quality basis sets, etc.). In our test calculations, single Slater determinants from density functional theory or Hartree–Fock calculations were used as trial wave functions, with no additional optimization. The calculated dissociation energies of various molecules and the cohesive energy of bulk Si are in excellent agreement with experiment and are comparable to or better than the best existing theoretical results.