Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

We extend our low-scaling variational Monte Carlo (VMC) algorithm to optimize the symmetry projected Jastrow mean field (SJMF) wavefunctions. These wavefunctions consist of a symmetryprojected product of a Jastrow and a general broken-symmetry mean field reference. Examples include Jastrow antisymmetrized geminal power (JAGP), Jastrow-Pfaffians, and resonating valence bond (RVB) states among others, all of which can be treated with our algorithm. We will demonstrate using benchmark systems including the nitrogen molecule, a chain of hydrogen atoms, and 2-D Hubbard model that a significant amount of correlation can be obtained by optimizing the energy of the SJMF wavefunction. This can be achieved at a relatively small cost when multiple symmetries including spin, particle number, and complex conjugation are simultaneously broken and projected. We also show that reduced density matrices can be calculated using the optimized wavefunctions, which allows us to calculate other observables such as correlation functions and will enable us to embed the VMC algorithm in a complete active space self-consistent field (CASSCF) calculation.arXiv:1902.07690v2 [cond-mat.str-el]

show abstract

“…Using the approach developed in Ref. 71, one can use Jastrow correlated wavefunctions in AFQMC as well.…”

Section: Discussionmentioning

confidence: 99%

Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo

Mahajan

Sharma

2019

J. Phys. Chem. A

View full text Add to dashboard Cite

show abstract

“…can improve accuracy, reduce time-step error, local energy fluctuations and the imaginary time needed to reach equilibration of walker ensembles (Al-Saidi, Chang, Rubenstein, & Morales, 2016). Other form of trial wave functions have also been used, including generalized valence bond (GVB) in molecules (Purwanto et al, 2008) and numberprojected Bardeen-Cooper-Schrieffer (BCS) trial wave functions in atomic gases (Carlson, Gandolfi, Schmidt, & Zhang, 2011).…”

Section: The Phaseless Approximationmentioning

confidence: 99%

“…Often using a single SD, such as the HF or DFT wave function, delivers results of excellent accuracy. Use of multideterminant trial wave functions:

∣ Ψ_{T} false〉 = \sum_{d = 1}^{N_{d}} A_{d} ∣ Ψ_{d} false〉

can improve accuracy, reduce time‐step error, local energy fluctuations and the imaginary time needed to reach equilibration of walker ensembles (Al‐Saidi, Zhang, & Krakauer, ; Chang, Rubenstein, & Morales, ). Other form of trial wave functions have also been used, including generalized valence bond (GVB) in molecules (Purwanto et al, ) and number‐projected Bardeen–Cooper–Schrieffer (BCS) trial wave functions in atomic gases (Carlson, Gandolfi, Schmidt, & Zhang, ).…”

Section: Constrained Afqmc Calculationsmentioning

confidence: 99%

Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method

Motta

Zhang

2018

WIREs Comput Mol Sci

133

215

View full text Add to dashboard Cite

The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independentelectron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming K E Y W O R D S ab initio methods, auxiliary-field quantum Monte Carlo, back-propagation, computational quantum chemistry, constrained path approximation, electronic structure, importance sampling, phase problem, phaseless approximation, quantum many-body computation, quantum Monte Carlo methods, sign problem 1 | INTRODUCTIONA central challenge in the fields of condensed matter physics, quantum chemistry (QC), and materials science is to determine the quantum mechanical behavior of many interacting electrons and nuclei. Often relativistic effects and the coupling between the dynamics of electrons and nuclei can be neglected, or treated separately. Within this approximation, the many-electron wave function can be found by solving the time-independent Schrödinger equation for the Born-Oppenheimer Hamiltonian

show abstract

“…It is thus important to have size-consistent alternatives. In addition to the single-determinant trial wave function, which has been shown to be very accurate in a large variety of systems, interesting possibilities exist with GHF and symmetry-restoration 42 , BCS 43 and HFB 17 , and a stochastic representation of Jastrow factors 59 . Recently a selfconsistent constraint has been proposed and shown to further reduce the systematic error from the constrained path approximation in lattice model calculations, especially in quantities such as spin and charge density and the reduced density matrix 45,60 .…”

Section: Self-consistent Afqmcmentioning

confidence: 99%

Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials

Shi,

Zhang

2020

Preprint

View full text Add to dashboard Cite

The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and algorithm of the method specialized for real materials, and present several recent developments. We give a systematic exposition of the key steps of AFQMC, closely tracking the framework of a modern software library we are developing. The building of a Monte Carlo Hamiltonian, projecting to the ground state, sampling two-body operators, phaseless approximation, and measuring ground state properties are discussed in details. An advanced implementation for multi-determinant trial wave functions is described which dramatically speeds up the algorithm and reduces the memory cost. We propose a self-consistent constraint for real materials, and discuss two flavors for its realization, either by coupling the AFQMC calculation to an effective independent-electron calculation, or via the natural orbitals of the computed one-body density matrix.

show abstract

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

Cited by 19 publications

References 44 publications

Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo

Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo

Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method

Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials

Contact Info

Product

Resources

About