NUMERICAL STABILITY AND THE SIGN PROBLEM IN THE DETERMINANT QUANTUM MONTE CARLO METHOD

2005 ◽  
Vol 16 (08) ◽  
pp. 1319-1327 ◽  
Author(s):  
E. Y. LOH ◽  
J. E. GUBERNATIS ◽  
R. T. SCALETTAR ◽  
S. R. WHITE ◽  
D. J. SCALAPINO ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Numerical Stability ◽  
Exact Diagonalization ◽  
Monte Carlo Algorithm ◽  
Numerical Accuracy ◽  
Numerical Errors ◽  
Sign Problem ◽  
Quantum Monte Carlo Method ◽  
D Wave

A recent paper by Matuttis and Ito questions the numerical accuracy of a widely-used fermion Monte Carlo algorithm. They also claim that the increase in the d-wave pairfield susceptibility χd(T) of a doped 4×4 Hubbard model at low temperature, previously found using this algorithm, is an artifact due to numerical errors. Here, we provide tests which show that this algorithm is numerically accurate and show that the simulation of χd for a 2×2 lattice agrees with exact diagonalization results. We also provide more complete data for χd on a 4×4 lattice that is consistent with our previous results.

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.

NEGATIVE WEIGHTS IN QUANTUM MONTE CARLO SIMULATIONS AT FINITE-TEMPERATURES USING THE AUXILIARY FIELD METHOD

1994 ◽  
Vol 05 (03) ◽  
pp. 599-613 ◽  
Author(s):  
J.E. GUBERNATIS ◽  
X.Y. ZHANG
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Topological Defects ◽  
Field Method ◽  
Monte Carlo Algorithm ◽  
Auxiliary Field ◽  
Sign Problem ◽  
Time Patterns ◽  
Ill Conditioned Matrices ◽  
Quantum Monte Carlo Simulations

We study the conditions under which negative weights (the sign problem) can exist in the finite-temperature, auxiliary field, quantum Monte Carlo algorithm of Blankenbecler, Scalapino, and Sugar. We specifically consider whether the sign problem arises from round-off error resulting from operations involving very ill-conditioned matrices or from topological defects in the auxiliary fields mirroring the space-time patterns of the physical fields. While we demonstrate these situations can generate negative weights, the results of our numerical tests suggest that these factors are most likely not the dominant sources of the problem. We also argue that the negative weights should not be considered as just a fermion problem. If it exists for the fermion problem, it will also exist for an analogous boson problem.

scholarly journals Amelioration for the Sign Problem: An Adiabatic Quantum Monte Carlo Algorithm

2021 ◽  
Vol 127 (21) ◽  
Author(s):  
Mohammad-Sadegh Vaezi ◽  
Amir-Reza Negari ◽  
Amin Moharramipour ◽  
Abolhassan Vaezi
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Sign Problem

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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