Phaseless Auxiliary-field Quantum Monte Research Articles

Response properties in phaseless auxiliary field quantum Monte Carlo.

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.

Phaseless auxiliary field quantum Monte Carlo with projector-augmented wave method for solids.

We implement the phaseless auxiliary field quantum Monte Carlo method using the plane-wave based projector augmented wave method and explore the accuracy and the feasibility of applying our implementation to solids. We use a singular value decomposition to compress the two-body Hamiltonian and, thus, reduce the computational cost. Consistent correlation energies from the primitive-cell sampling and the corresponding supercell calculations numerically verify our implementation. We calculate the equation of state for diamond and the correlation energies for a range of prototypical solid materials. A down-sampling technique along with natural orbitals accelerates the convergence with respect to the number of orbitals and crystal momentum points. We illustrate the competitiveness of our implementation in accuracy and computational cost for dense crystal momentum point meshes compared to a well-established quantum-chemistry approach, the coupled-cluster ansatz including singles, doubles, and perturbative triple particle-hole excitation operators.

Selected configuration interaction wave functions in phaseless auxiliary field quantum Monte Carlo

We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward optimizing computational performance for longer configuration interaction expansions, allow us to use up to a million configurations in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about 3 for a calculation with 104 configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in auxiliary field quantum Monte Carlo calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors.

Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo.

We present an ab initio auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the ab initio phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, ab initio finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for H2O (STO-3G), C2 (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multiorbital Hubbard model. Our method effectively controls the phase problem through importance sampling, often even without invoking the phaseless approximation, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.

Imaginary time density-density correlations for two-dimensional electron gases at high density.

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

The phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.

Auxiliary-field quantum Monte Carlo study of TiO and MnO molecules

Calculations of the binding energy of the transition metal oxide molecules TiO and MnO are presented, using a recently developed phaseless auxiliary field quantum Monte Carlo approach. This method maps the interacting many-body problem onto a linear combination of non-interacting problems by a complex Hubbard-Stratonovich transformation, and controls the phase/sign problem with a phaseless approximation relying on a trial wave function. It employs random walks in Slater determinant space to project the ground state of the system, and allows use of much of the same machinery as in standard density functional theory calculations, such as planewave basis and non-local pseudopotentials. The calculations used a single Slater determinant trial wave function obtained from a density functional calculation, with no further optimization. The calculated binding energies are in good agreement with experiment and with recent diffusion Monte Carlo results. Together with previous results for sp-bonded systems, the present study indicates that the phaseless auxiliary field method is a robust and promising approach for the study of correlation effects in real materials.