Calculation of ground state energy of a “4 × 4” flux qubit Josephson junction array using diffusion quantum Monte Carlo method

2013 ◽  
Author(s):  
Tiem Leong Yoon ◽  
Eong Sheng Goh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Josephson Junction ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
State Energy ◽  
Josephson Junction Array ◽  
Junction Array ◽  
Quantum Monte Carlo Method ◽  
Flux Qubit

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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