Search Results for « Finite Temperature Auxiliary Field Quantum Monte Carlo (AFQMC) »

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Noncovalent interactions are ubiquitous in chemistry and play key roles in, e.g., drug-protein interactions, secondary-sphere effects in catalysis, molecular crystals, the structure of biomolecules, and the properties of liquids. However, their description with approximate electronic structure models is a long standing challenge due to the manybody correlation effects, relatively small energy scales, and potentially large system sizes involved. In this work we first assess the simplest phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) model, which uses restricted Hartree-Fock trial wavefunctions, for representative test sets of noncovalent interactions such as hydrogen bonding, electrostatics, and dispersion (S66, A24, S22, and X31). Against CCSD(T) reference values, we find accuracy consistently better than CCSD, and sometimes dramatically better than MP2. In addition, we use the water dimer (with available CCSDTQ reference energies) to demonstrate that noncovalent interaction energies calculated with ph-AFQMC-RHF benefit significantly from error cancellation. In this spirit, we further show how a branching correlated sampling scheme can be used to reduce the computational cost of noncovalent interaction energy calculations, paving the way to more tractable ph-AFQMC studies of larger molecules.