Quantum Monte Carlo Optimization in Many Fermion Systems

2006 ◽  
Author(s):  
Takashi Yanagisawa
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Optimization ◽  
Fermion Systems

scholarly journals Self-learning quantum Monte Carlo method in interacting fermion systems

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Xiao Yan Xu ◽  
Yang Qi ◽  
Junwei Liu ◽  
Liang Fu ◽  
Zi Yang Meng
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Fermion Systems ◽  
Quantum Monte Carlo Method ◽  
Self Learning

Optimization of quantum Monte Carlo wavefunctions using analytical derivatives

1992 ◽  
Vol 70 (2) ◽  
pp. 366-371 ◽  
Author(s):  
Hartmut Bueckert ◽  
Stuart M. Rothstein ◽  
Jan Vrbik
Keyword(s):  
Monte Carlo ◽  
Electron Correlation ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Numerical Evaluation ◽  
Monte Carlo Optimization ◽  
Technical Issues ◽  
Numerical Performance ◽  
Analytical Derivatives ◽  
State Wavefunctions

We show how to optimize many-parameter wavefunctions for use in quantum Monte Carlo by deriving and utilizing formulas for analytical rather than numerical evaluation of the required derivatives. We present these in a form which is easily vectorizable for use on a supercomputer. We also discuss several technical issues of variational Monte Carlo to ensure both an unbiased and efficient optimization. Finally, we illustrate our optimization scheme's numerical performance by optimizing ground-state wavefunctions for LiH and H2O, each with more than 100 variational parameters. Keywords: quantum Monte Carlo, optimization, electron correlation, LiH, H2O.

MONTE CARLO DIAGONALIZATION OF VERY LARGE MATRICES: APPLICATION TO FERMION SYSTEMS

1992 ◽  
Vol 03 (01) ◽  
pp. 97-104 ◽  
Author(s):  
H. DE RAEDT ◽  
W. VON DER LINDEN
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
General Feature ◽  
Degrees Of Freedom ◽  
Fundamental Problem ◽  
Simulation Methods ◽  
Fermion Systems ◽  
Monte Carlo Algorithms ◽  
Minus Sign ◽  
Sign Problem

All known Quantum-Monte-Carlo algorithms for fermions suffer from the so-called “minus-sign-problem” which is detrimental to the application of these simulation methods to fermion systems at very low temperatures and/or of very many lattice sites. We identify the origin of this fundamental problem, demonstrate that it is a very general feature, not necessarily related to the presence of fermionic degrees of freedom. We describe an novel algorithm which does not suffer from the minus-sign problem. Illustrative results for the two-dimensional Hubbard model are presented

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