# Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure

@article{Motta2019HamiltonianSI, title={Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure}, author={Mario Motta and Shiwei Zhang and Garnet Kin-Lic Chan}, journal={Physical Review B}, year={2019} }

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo (AFQMC) calculations. Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by N^(-1)_k, where N_k is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides…

## 15 Citations

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- ChemistryThe Journal of chemical physics
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Recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus are reviewed and a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets are utilized.

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- PhysicsJournal of chemical theory and computation
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- 2020

With intuition aided by tensor diagrams, irreducible representation alignment is presented, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms.

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- Computer ScienceThe Journal of chemical physics
- 2020

The theoretical framework developed here should facilitate large-scale ph-AFQMC applications that were previously difficult or impossible to carry out with standard computational resources.

## References

SHOWING 1-10 OF 103 REFERENCES

Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians.

- PhysicsPhysical review letters
- 2015

A combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects.

Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

Results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas are shown using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function.

Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo.

- PhysicsJournal of chemical theory and computation
- 2017

A modified BP method for the computation of observables in electronic systems is proposed, its numerical stability and computational complexity are discussed, and its performance by computing ground-state properties in several molecular systems, including small organic molecules is assessed.

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

- Chemistry
- 2017

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…

Quantum Monte Carlo method for the ground state of many-boson systems.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

A quantum Monte Carlo method for calculating the ground state of many-boson systems, based on a field-theoretical approach, that provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of noninteracting solutions.

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide.

- PhysicsThe Journal of chemical physics
- 2018

This article investigates the application of AFQMC to realistic strongly correlated materials in periodic Gaussian basis sets using nickel oxide (NiO) as an example and investigates the importance of finite size effects and basis set errors on the structural properties of the correlated solid.

Quantum Monte Carlo method using phase-free random walks with slater determinants.

- PhysicsPhysical review letters
- 2003

A quantum Monte Carlo method for many fermions using random walks in the space of Slater determinants is developed, and the calculated binding energies of dimers and cohesive energy of bulk Si are comparable to the best existing theoretical results.

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group

- Physics
- 2002

We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yield…

Separable dual-space Gaussian pseudopotentials.

- PhysicsPhysical review. B, Condensed matter
- 1996

The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set and is separable and has optimal decay properties in both real and Fourier space.