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.

STUDY OF PHASE SEPARATION IN THE HUBBARD MODEL1

1991 ◽  
Vol 05 (01n02) ◽  
pp. 113-118
Author(s):  
A. Moreo
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Repulsive Interaction ◽  
Two Dimensional ◽  
Quantum Monte Carlo Method ◽  
The Mean ◽  
Number Of Particles

We study the behavior of the mean number of particles <n> as a function of the chemical potential μ in the two dimensional Hubbard model with both attractive and repulsive interaction, using a quantum Monte Carlo method. Working at U/t=10, 4 and −4 on lattices with 4×4, 6×6 and 8×8 sites, we do not find evidence of phase separation.

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.

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 Imaginary-chemical-potential quantum Monte Carlo method for Hubbard molecules

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Fei Lin ◽  
Jurij Šmakov ◽  
Erik S. Sørensen ◽  
Catherine Kallin ◽  
A. John Berlinsky
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Quantum Monte Carlo Method
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