Linear-scaling fixed-node diffusion quantum Monte Carlo: Accounting for the nodal information in a density matrix-based scheme

2008 ◽  
Vol 128 (13) ◽  
pp. 134104 ◽  
Author(s):  
Jörg Kussmann ◽  
Christian Ochsenfeld
Keyword(s):  
Monte Carlo ◽  
Density Matrix ◽  
Quantum Monte Carlo ◽  
Linear Scaling ◽  
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

scholarly journals Density-matrix quantum Monte Carlo method

2014 ◽  
Vol 89 (24) ◽  
Author(s):  
N. S. Blunt ◽  
T. W. Rogers ◽  
J. S. Spencer ◽  
W. M. C. Foulkes
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Density Matrix ◽  
Quantum Monte Carlo ◽  
Quantum Monte Carlo Method ◽  
Matrix Quantum

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.

Quantum Monte Carlo with density matrix: potential energy curve derived properties

2017 ◽  
Vol 23 (4) ◽  
Author(s):  
Víctor S. Bonfim ◽  
Nádia M. Borges ◽  
João B. L. Martins ◽  
Ricardo Gargano ◽  
José Roberto dos S. Politi
Keyword(s):  
Monte Carlo ◽  
Potential Energy ◽  
Density Matrix ◽  
Quantum Monte Carlo ◽  
Potential Energy Curve ◽  
Energy Curve ◽  
Matrix Potential ◽  
Derived Properties
Sign in / Sign up

Export Citation Format

Share Document