Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

Abstract

We investigate the use of interpolative separable density fitting (ISDF) as a means to reduce the memory bottleneck in auxiliary field quantum Monte Carlo (AFQMC) simulations of real materials in Gaussian basis sets. We find that ISDF can reduce the memory scaling of AFQMC simulations from O(M 4 ) to O(M 2 ). We test these developments by computing the structural properties of Carbon in the diamond phase, comparing to results from existing computational methods and experiment. the choice of approximate exchange correlation functional. Calculating band gaps in semiconductors 1 , discerning different phases in hydrogen under extreme conditions, 2-4 and the systematic description of strongly correlated materials 5 are some well known limitations of DFT. The development of hybrid functionals 6-10 and adaptations of the exchange-correlation functional for strong correlations 11 can sometimes improve results, but require an often adhoc determination of additional parameters.Wavefunction based quantum chemical methods offer an alternative, systematic approach to solving the electronic structure problem directly. Unfortunately, they come with a cost which is often prohibitively large. For example, standard Coupled-Cluster theory (including single and double excitations) scales like the sixth power of the system size, while the exact approach of FCI scales exponentially. Nevertheless, they are increasingly and successfully being applied to problems in solid state physics 12-17 .Quantum Monte Carlo (QMC) methods offer another route to directly solving the manyelectron Schrödinger equation, with often much more favorable scaling. Real space diffusion Monte Carlo 18 is perhaps the most widely used QMC approach to solving electronic structure problems, and can now routinely simulate 100s to 1000s of atoms, making full use of modern supercomputers. 19 In order to overcome the fermionic sign problem, DMC uses a trial wavefunction to impose the fixed-node approximation. Although results for the uniform electron gas suggest that the fixed-node approximation is extremely accurate 20 , it is often difficult to improve the nodes for more realistic systems, where the nodal error can be more significant.Additionally, non-local pseudopotentials, which are eventually necessary for describing heavier elements, are difficult to use and require additional uncontrolled approximations (e.g. the locality approximations 21 ) which are also hard to assess and improve.Phaseless auxiliary field QMC 22,23 (AFQMC) offers an alternative route to overcoming some of these issues. Similar to DMC, it also uses a constraint to remove the fermion sign problem at the expense of a bias 22 , which it implements with a trial wavefunction.Multi-determinant 24,25 , generalized Hartree-Fock 24,26 , and self-consistently determined trial

Taming the sign problem in auxiliary field quantum Monte Carlo using accurate trial wave functions

“…Many ways of reducing this cost in AFQMC have been proposed for single determinant and multi-Slater trials. [37][38][39][40][41] Below we will describe economic algorithms for evaluating local energies for multi-Slater and symmetry projected mean-fields trial states which can be used as |ψ l . To use a wave function as the trial state |ψ r in the sampling method outlined in the last section, one needs to be able to sample a determinant from it (equation 13).…”

In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

“…It has recently been shown to produce accurate triplet energies for all linear polyacenes with experimentally reported T1 energies (naphthalene through pentacene) as well as for biradicals. 53 Recent algorithmic advances [54][55][56][57] have greatly reduced the computational costs of this methodology, enabling its use in the accurate prediction of novel chromophores, even those which may be strongly-correlated.…”

In-Silico Prediction of Annihilators for Triplet Fusion Upconversion via Auxiliary-Field Quantum Monte Carlo

“…It has recently been shown to produce accurate triplet energies for all linear polyacenes with experimentally reported T1 energies (naphthalene through pentacene) as well as for biradicals. 54 Recent algorithmic advances [55][56][57][58] have greatly reduced the computational costs of this methodology, enabling its use in the accurate prediction of novel chromophores, even those which may be strongly-correlated.…”