scholarly journals MULTILEVEL BLOCKING MONTE CARLO SIMULATIONS FOR QUANTUM DOTS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1416-1425 ◽  
Author(s):  
R. EGGER ◽  
C. H. MAK
Keyword(s):  
Quantum Dots ◽  
Monte Carlo ◽  
Low Temperature ◽  
Monte Carlo Simulations ◽  
Strongly Correlated Electrons ◽  
Correlated Electrons ◽  
Strongly Correlated ◽  
Path Integral Monte Carlo ◽  
Sign Problem ◽  
Simulation Results

This article provides an introduction to the ideas behind the multilevel blocking (MLB) approach to the fermion sign problem in path-integral Monte Carlo simulations, and also gives a detailed discussion of MLB results for quantum dots. MLB can turn the exponential severity of the sign problem into an algebraic one, thereby enabling numerically exact studies of otherwise inaccessible systems. Low-temperature simulation results for up to eight strongly correlated electrons in a parabolic 20 quantum dot are presented.

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.

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