scholarly journals Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration

2020 ◽  
Vol 153 (23) ◽  
pp. 234104
Author(s):  
Tobias Dornheim ◽  
Michele Invernizzi ◽  
Jan Vorberger ◽  
Barak Hirshberg
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
Thermodynamic Integration ◽  
Path Integral Monte Carlo ◽  
Sign Problem ◽  
Bogoliubov Inequality

scholarly journals Monte Carlo simulations of the electron short-range quantum ordering in Coulomb systems and the “fermionic sign problem”.

2021 ◽  
Author(s):  
Vladimir S Filinov ◽  
Pavel Levashov ◽  
Alexander Larkin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
Short Range ◽  
Coulomb Systems ◽  
Thermodynamic Characteristics ◽  
Distribution Functions ◽  
Path Integral Monte Carlo ◽  
Path Integral Representation ◽  
Sign Problem

Abstract To account for the interference effects of the Coulomb and exchange interactions of electrons the new path integral representation of the density matrix has been developed in the canonical ensemble at finite temperatures. The developed representation allows to reduce the notorious ``fermionic sign problem'' in the path integral Monte Carlo simulations of fermionic systems. The obtained results for pair distribution functions in plasma and uniform electron gas demonstrate the short--range quantum ordering of electrons associated in literature with exchange--correlation excitons. The charge estimations show the excitonic electric neutrality. Comparison of the internal energy with available ones in the literature demonstrates that the short range ordering does not give noticeable contributions in integral thermodynamic characteristics. This fine physical effect was not observed earlier in the standard path integral Monte Carlo simulations.

Constructing accurate interaction potentials to describe the microsolvation of protonated methane by helium atoms

2017 ◽  
Vol 19 (12) ◽  
pp. 8307-8321 ◽  
Author(s):  
Dennis Kuchenbecker ◽  
Felix Uhl ◽  
Harald Forbert ◽  
Georg Jansen ◽  
Dominik Marx
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Ab Initio ◽  
Path Integral ◽  
Interaction Potential ◽  
Stationary Point ◽  
Path Integral Monte Carlo ◽  
Interaction Potentials ◽  
Helium Atoms

An ab initio-derived interaction potential is derived and used in path integral Monte Carlo simulations to investigate stationary-point structures of CH5+ microsolvated by up to four helium atoms.

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

2013 ◽  
Vol 12 (04) ◽  
pp. 1350026 ◽  
Author(s):  
MARCIN BUCHOWIECKI
Keyword(s):  
Monte Carlo ◽  
Temperature Dependence ◽  
Equilibrium Constant ◽  
Path Integral ◽  
Thermodynamic Integration ◽  
Partition Functions ◽  
Integration Path ◽  
Path Integral Monte Carlo

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

Path integral Monte Carlo simulations: Study of the efficiency of energy estimators

1995 ◽  
Vol 103 (13) ◽  
pp. 5720-5724 ◽  
Author(s):  
Pedro Alexandrino Fernandes ◽  
Alfredo Palace Carvalho ◽  
J. P. Prates Ramalho
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
Path Integral Monte Carlo

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992 ◽  
Vol 03 (02) ◽  
pp. 337-346 ◽  
Author(s):  
D. MARX ◽  
P. NIELABA ◽  
K. BINDER
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
General Relation ◽  
Absolute Magnitude ◽  
Computational Effort ◽  
Imaginary Time ◽  
Time Dimension ◽  
Path Integral Monte Carlo

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator has the advantage of being based directly on the energy estimatorand thus requires no extra computational effort and is suited for extensive phase diagramstudies. As an example, numerical results are presented for a two-dimensional fluid withinternal magnetic quantum degrees of freedom. We discuss in detail origin and consequences of the excess term. Due to the subtraction of two relatively large contributions ofsimilar absolute magnitude a large statistical effort would be necessary for very accurateheat capacity estimates.

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