scholarly journals Adaptive sampling approach to the negative-sign problem in the auxiliary-field quantum Monte Carlo method

2000 ◽  
Vol 62 (16) ◽  
pp. 10674-10679 ◽  
Author(s):  
Yoshihiro Asai
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Adaptive Sampling ◽  
Negative Sign ◽  
Auxiliary Field ◽  
Sign Problem ◽  
Quantum Monte Carlo Method ◽  
Sampling Approach

scholarly journals Auxiliary-field quantum Monte Carlo method for strongly paired fermions

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
J. Carlson ◽  
Stefano Gandolfi ◽  
Kevin E. Schmidt ◽  
Shiwei Zhang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Auxiliary Field ◽  
Quantum Monte Carlo Method

scholarly journals QUANTUM MONTE CARLO METHOD APPLIED TO STRONGLY CORRELATED DILUTE FERMI GASES WITH FINITE EFFECTIVE RANGE

2009 ◽  
Vol 18 (04) ◽  
pp. 919-925 ◽  
Author(s):  
GABRIEL WLAZŁOWSKI ◽  
PIOTR MAGIERSKI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Exact Diagonalization ◽  
Effective Range ◽  
Fermi Gases ◽  
Strongly Correlated ◽  
Sign Problem ◽  
Quantum Monte Carlo Method

We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method applied to dilute neutron matter at finite temperatures. We formulate the discrete Hubbard-Stratonovich transformation for the interaction with finite effective range which is free from the sign problem. The AFQMC results are compared with those obtained from exact diagonalization for a toy model. Preliminary calculations of energy and chemical potential as a function of temperature are presented.

scholarly journals Comparison of Calculations for the Hubbard Model Obtained with Quantum-Monte-Carlo, Exact, and Stochastic Diagonalization

1997 ◽  
Vol 08 (02) ◽  
pp. 397-415 ◽  
Author(s):  
Thomas Husslein ◽  
Werner Fettes ◽  
Ingo Morgenstern
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Hubbard Model ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Minus Sign ◽  
Sign Problem ◽  
Quantum Monte Carlo Method ◽  
Convergence Problems ◽  
Superconducting Correlations

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the influence of the minus sign problem on convergence. Also here in the absence of a minus sign problem we encounter convergence problems for strong interactions.

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