A Study on Variational Monte Carlo of Attractive Hubbard Model

Abstract

The analysis of the Hubbard model with the wave function of Gutzwiller is proposed to include a variational Monte-Carlo system that combines variational theory with Monte-Carlo method. One, two and three-dimensional models of sites of up to 216 (6×6×6) are applied and arbitrary U/t values (site U and hopping integral t) are applied. In order to accurately measure the expectation values for many multi-body wavefunctions, a series of variational calculations with Monte Carlo better statistics were carried out. Simulations of Quantum Monte Carlo (QMC) are a powerful way of obtaining knowledge on quantum mechanical systems with strong interactions. In this paper, we start by presenting the model of Hubbard and the quantum simulation of Monte Carlo. The Hubbard model is a simple and efficient model that effectively captures several qualitative elements of materials, including metal transition monoxides and superconductors with high temperatures.