Path integral Monte Carlo benchmarks for two-dimensional quantum dots

We report numerically accurate path integral Monte Carlo results for harmonically confined two-dimensional quantum dots containing up to $N=60$ interacting electrons. The finite-temperature values are extrapolated to 0 K and zero time step in order to provide precise upper-bound energies. The ground-state energies are compared against coupled-cluster and diffusion Monte Carlo results available in the literature for $N\le 20$. We also provide Padé fits for the energies as a function of $N$ for different strengths of the confining potential. The fits deviate less than $0.25\%$ from the path integral Monte Carlo data. Overall, our upper-bound estimates for the ground-state energies have lower values than previous diffusion Monte Carlo benchmarks due to the accurate nodal surface in our simulations. Hence, our results set a new numerical benchmark for two-dimensional (spin-unpolarized) quantum dots up to a large number of electrons.

Figure 1

Scaling relation of the ground-state energy from Ref. [18] (solid line) and path integral Monte Carlo data with three different confinement strengths (symbols). Large-$N$ values tend towards the Padé form of the scaling function as expected.

Figure 2

Modified Padé fits to our PIMC data; see Eq. (3). The fits yield better than $0.24\%$ accuracy with respect to our PIMC data, and on average the discrepancy is less than $0.1\%$. The PIMC data points correspond to $N=6$, 12, 20, 40, and 60, and the energy values are shown in Table 4.