# Implementation of the linear method for the optimization of Jastrow-Feenberg and backflow correlations

@article{Motta2015ImplementationOT,
title={Implementation of the linear method for the optimization of Jastrow-Feenberg and backflow correlations},
author={Mario Motta and G. Bertaina and Davide Emilio Galli and Ettore Vitali},
journal={Comput. Phys. Commun.},
year={2015},
volume={190},
pages={62-71}
}
• M. Motta, +1 author E. Vitali
• Published 1 December 2014
• Physics, Computer Science
• Comput. Phys. Commun.
Abstract We present a fully detailed and highly performing implementation of the Linear Method (Toulouse and Umrigar, 2007) to optimize Jastrow–Feenberg and Backflow Correlations in many-body wave-functions, which are widely used in condensed matter physics. We show that it is possible to implement such optimization scheme performing analytical derivatives of the wave-function with respect to the variational parameters achieving the best possible complexity O ( N 3 ) in the number of particles…
3 Citations

## Figures, Tables, and Topics from this paper

Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo
• Physics
• 2018
Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum
Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons
• Physics
• 2016
We compute several ground-state properties and the dynamical structure factor of a zero-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact
Imaginary time density-density correlations for two-dimensional electron gases at high density.
• Physics, Medicine
The Journal of chemical physics
• 2015
This work evaluates 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, and performs the inverse Laplace transform of the obtained density- density correlation functions.

## References

SHOWING 1-10 OF 76 REFERENCES
Alleviation of the Fermion-sign problem by optimization of many-body wave functions
• Physics
• 2007
We present a simple, robust, and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice
Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules.
• Physics, Medicine
The Journal of chemical physics
• 2008
The linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits it to extend it to minimize a linear combination of the energy and the energy variance.
Wave function optimization in the variational Monte Carlo method
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the
Variational Monte Carlo calculations of liquid /sup 4/He with three-body correlations
• Physics
• 1980
The first Monte Carlo calculations explicitly employing triplet correlations in the variational wave function for the ground state of $^{4}\mathrm{He}$ are presented. A significant lowering of energy
Energy and variance optimization of many-body wave functions.
• Mathematics, Medicine
Physical review letters
• 2005
A simple, robust, and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy, which is compared to what is currently the most popular method for optimizing many- body wave functions, namely, minimization of the variance of the local energy.
Structure of the ground state of a fermion fluid
• Physics
• 1981
Variational many-body wave functions for the ground state of liquid /sup 3/He which include triplet and backflow correlations are investigated with use of Monte Carlo integration. Our energy of
Inhomogeneous backflow transformations in quantum Monte Carlo calculations.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2006
It is found that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations.
The Collective Treatment of Many-body Systems: III
In a previous paper a trial wave function of the form ψ = DIIi<if(xij) was used variationally to calculate the ground-state energy of an interacting electron gas, D being a determinant of plane waves
The Collective Treatment of a Fermi Gas: II
The ground state energy of the free electron gas is calculated using the Rayleigh-Schrodinger variational method with the wave function ψ=DΠi<jf(xij) where D is a determinant of plane waves and
Fermion Monte Carlo algorithms and liquid 3He.
• Physics, Medicine
Physical review letters
• 1989
The first mirror potential GFMC calculations in a many-fermion problem are reported, comparing them with transient estimation and fixed-node studies to illustrate the strengths and weaknesses of each.