## Path integral Monte Carlo benchmarks for two-dimensional quantum dots

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**Path integral Monte Carlo benchmarks for two-dimensional quantum dots.** / Kylänpää, Ilkka; Räsänen, Esa.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Physical Review B*, vol. 96, no. 20, 205445. https://doi.org/10.1103/PhysRevB.96.205445

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*Physical Review B*,

*96*(20), [205445]. https://doi.org/10.1103/PhysRevB.96.205445

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TY - JOUR

T1 - Path integral Monte Carlo benchmarks for two-dimensional quantum dots

AU - Kylänpää, Ilkka

AU - Räsänen, Esa

PY - 2017/11/30

Y1 - 2017/11/30

N2 - 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≤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.

AB - 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≤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.

U2 - 10.1103/PhysRevB.96.205445

DO - 10.1103/PhysRevB.96.205445

M3 - Article

VL - 96

JO - Physical Review B

JF - Physical Review B

SN - 1098-0121

IS - 20

M1 - 205445

ER -