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 $\mathcal{O}(M^4)$ to $\mathcal{O}(M^2)$. We test these developments by computing the structural properties of Carbon in the diamond phase, comparing to results from existing computational methods and experiment.

arXiv commentAccepted Version

References in corpus (34)

• Separable Dual Space Gaussian Pseudo-potentials
• Quasiparticle Self-Consistent GW Theory
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• A Constrained Path Monte Carlo Method for Fermion Ground States
• Twist-averaged Boundary Conditions in Continuum Quantum Monte Carlo
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Finite-size errors in continuum quantum Monte Carlo calculations
• Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
• Finite-size correction in many-body electronic structure calculations
• Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
• Gaussian and plane-wave mixed density fitting for periodic systems
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Benchmark of Exchange-Correlation Functionals for High Pressure Hydrogen using Quantum Monte Carlo
• Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules
• Fate of density functional theory in high-pressure solid hydrogen
• Quantum Monte Carlo method for the ground state of many-boson systems
• Wavefunction-based correlated ab initio calculations on crystalline solids
• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets
• Phaseless Auxiliary-Field Quantum Monte Carlo on Graphical Processing Units
• Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo
• Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo
• Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
• Excited state calculations in solids by auxiliary-field quantum Monte Carlo
• Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo
• Ultracold atoms in a square lattice with spin-orbit coupling: Charge order, superfluidity, and topological signatures
• Imaginary Time Correlations and the phaseless Auxiliary Field Quantum Monte Carlo
• Finite-size correction in many-body electronic structure calculations of magnetic systems
• Multi-determinant generalized Hartree-Fock wave functions in Monte Carlo calculations
• Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting

Cited by in corpus (24)

• QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
• Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C${}_{36}$ Fullerene and an Iron Porphyrin Model Complex
• Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Unit
• Interpolative separable density fitting decomposition for accelerating Hartree-Fock exchange calculations within numerical atomic orbitals
• Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
• The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene
• Stochastic Resolution-of-the-Identity Auxiliary-Field Quantum Monte Carlo: Scaling Reduction without Overhead
• Systematic Comparison and Cross-validation of Fixed-Node Diffusion Monte Carlo and Phaseless Auxiliary-Field Quantum Monte Carlo in Solids
• Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling
• Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction
• Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules
• Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans' Theorem Approach
• Accelerating the Convergence of Auxiliary-Field Quantum Monte Carlo inSolids with Optimized Gaussian Basis Sets
• Toward an accurate equation of state and B1-B2 phase boundary for magnesium oxide to TPa pressures and eV temperatures
• Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems
• Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework
• Block Tensor Decomposition: A dual grid scheme with formal O(N3) for THC decomposition of molecular systems
• Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting
• Efficient Auxiliary-Field Quantum Monte Carlo using Isometric Tensor Hypercontraction