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During the stochastic optimization for the one-body parameters in (Equation presented), the electron occupation in (Equation presented) points generally changes when (Equation presented) is chosen as the ground state of (Equation presented). The change of electron configurations often causes the stochastic optimization to be unstable. To avoid this, we perform the stochastic optimization with keeping an electron occupation in (Equation presented) points. Considering several possible electron occupations separately, we determine the optimized variational state with the lowest variational energy. Even though the electron occupation in (Equation presented) points is fixed during the stochastic optimization, we have found that the optimized variational state is always the ground state of (Equation presented) with the optimized variational parameters. Note that this problem does not occur when the Gutzwiller-Jastrow parameters are stochastically optimized.
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