Performance of the coupled-cluster singles and doubles method applied to two-dimensional quantum dots

An implementation of the coupled-cluster single and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches, including another CCSD implementation, for up to twelve confined electrons. The possibility to effectively use a very large basis set is found to be an important advantage compared to full configuration interaction implementations. The error in the ground-state energy introduced by truncating at triple excitations is shown to be comparable to the difference between the results from the variation and diffusion Monte Carlo methods. Convergence of the iterative solution of the coupled cluster equations is found for surprisingly weak confinement strengths even when the full electron-electron interaction is treated as a perturbation. The relevance of the omitted excitations is investigated through comparison with full configuration interaction results.

Figure 1

Total energies for a six electron $\hslash \omega =11.85720$ meV harmonic oscillator potential, truncating the basis by the $n$ and $|m_l|$ quantum numbers, displaying the convergence in the $|m_l|$ dimension, for $n=[4,5,6,8]$. The data points in this figure are identical to the ones in Fig. 2.

Figure 2

Total energies for a six electron $\hslash \omega =11.85720$ meV harmonic oscillator potential, truncating the basis by the $n$ and $|m_l|$ quantum numbers, displaying the convergence in the $n$ dimension, for $|m_l|=[6,7,8,9]$. The data points in this figure are identical to the ones in Fig. 1.

Figure 3

The energy for a two electron $\hslash \omega =11.85720$ meV harmonic oscillator potential. The stars are results from running the CCSD routine using $n$ and $|m_l|$ truncation. The stars on the finely dashed (blue) line are truncated at $|m_l|=1$ and for the set $n=[2:20,25,29]$, with the line being a fit to match these. The stars on the full (red) lines are truncated at the $n$ value from which they start, i.e., $n=[5,10,15,20,25,29]$, with an increasing $|m_l|$ value. The dashed lines continuing from the full line and the dotted line continuing from the finely dashed line are the extrapolated energies in the corresponding dimensions. The final extrapolated energy for $n=29$ and $|m_l|=30$ is $E=3.000089638$ a.u.*