scholarly journals Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo

2017 ◽  
Vol 146 (24) ◽  
pp. 244101 ◽  
Author(s):  
Jaron T. Krogel ◽  
P. R. C. Kent
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Localization Errors ◽  
Fixed Node

scholarly journals Phase separation in the two-dimensional Hubbard model: A fixed-node quantum Monte Carlo study

1998 ◽  
Vol 58 (22) ◽  
pp. R14685-R14688 ◽  
Author(s):  
A. C. Cosentini ◽  
M. Capone ◽  
L. Guidoni ◽  
G. B. Bachelet
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Hubbard Model ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Two Dimensional ◽  
Fixed Node

QUANTUM MONTE CARLO SIMULATIONS OF FERMIONS: A MATHEMATICAL ANALYSIS OF THE FIXED-NODE APPROXIMATION

2006 ◽  
Vol 16 (09) ◽  
pp. 1403-1440 ◽  
Author(s):  
ERIC CANCÈS ◽  
BENJAMIN JOURDAIN ◽  
TONY LELIÈVRE
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Mathematical Analysis ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Stochastic Methods ◽  
Sampling Function ◽  
Long Time ◽  
Nodal Surfaces ◽  
Fixed Node

The Diffusion Monte Carlo (DMC) method is a powerful strategy to estimate the ground state energy E0 of an N-body Schrödinger Hamiltonian H = -½Δ + V with high accuracy. It consists of writing E0 as the long-time limit of an expectation value of a drift-diffusion process with a source term, and numerically simulating this process by means of a collection of random walkers. As for a number of stochastic methods, a DMC calculation makes use of an importance sampling function ψI which hopefully approximates some ground state ψ0 of H. In the fermionic case, it has been observed that the DMC method is biased, except in the special case when the nodal surfaces of ψI coincide with those of a ground state of H. The approximation due to the fact that, in practice, the nodal surfaces of ψI differ from those of the ground states of H, is referred to as the Fixed Node Approximation (FNA). Our purpose in this paper is to provide a mathematical analysis of the FNA. We prove that, under convenient hypotheses, a DMC calculation performed with the importance sampling function ψI, provides an estimation of the infimum of the energy 〈ψ, Hψ〉 on the set of the fermionic test functions ψ that exactly vanish on the nodal surfaces of ψI.

GROUND-STATE PROPERTIES OF SMALL 3He DROPS FROM QUANTUM MONTE CARLO SIMULATIONS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2124-2133
Author(s):  
ESTER SOLA ◽  
JOAQUIM CASULLERAS ◽  
JORDI BORONAT
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Maximum Value ◽  
The Stability ◽  
Quantum Monte Carlo Simulations ◽  
Fixed Node ◽  
Structure Properties

We present recent results from a diffusion Monte Carlo study of small 3 He drops in the limit of zero temperature. Using the same methodology than in previous calculations carried out for bulk 3 He , we have obtained accurate results for their energy and structure properties. A relevant concern of this analysis has been the determination of the stability threshold for self binding. Our results show that the smallest self-bound drop is formed by N = 30 atoms, with preferred orbitals for open shells corresponding to maximum value of the spin. The quality of the upper bound energies provided by the fixed node approximation is analyzed by performing released-node estimations for short released times. Possible improvements of the nodal surface by including BCS-like correlation functions are also discussed.

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