arXiv:1905.07802 · Physical review. B./Physical review. B

Path-integral Monte Carlo study of electronic states in quantum dots in an external magnetic field

Csaba Tőke, Tamás Haidekker Galambos

Published Oct 21, 2019• 1 citation

Abstract

We explore the correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but sometimes the correlations saturate with decreasing temperature, providing insight into the ground-state properties.

DOI: 10.1103/physrevb.100.165136

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arXiv:1905.07802 · Physical review. B./Physical review. B

Path-integral Monte Carlo study of electronic states in quantum dots in an external magnetic field

Csaba Tőke, Tamás Haidekker Galambos

Published Oct 21, 2019• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.100.165136

Related papers

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Jan 1, 20010 citations

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 $N\ensuremath{\le}20$. We also provide Pad\'e 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.

We consider circular and elliptic quantum dots with parabolic external confinement, containing 0--22 electrons and with values of

{r}_{s}

in the range

0<{r}_{s}<3

. We perform restricted and unrestricted Hartree-Fock calculations, and further take into account electron correlations using second-order perturbation theory. We demonstrate that in many cases correlations qualitatively change the spin structure of the ground state from that obtained under Hartree-Fock and spin-density-functional calculations. In some cases the correlation effects destroy Hund's rule. We also demonstrate that the correlations destroy static spin-density waves observed in Hartree-Fock and spin-density-functional calculations.

We study

{N}_{e}

interacting electrons confined in a one-dimensional quantum ring (QR) first by using a Hartree-Fock approximation and then by introducing correlation effects. An external magnetic field

B

perpendicular to the ring plane is considered. The energy spectra of low-lying states of the QR as a function of

B

and

{N}_{e}

are obtained. A phase diagram is presented indicating a rich variety of ground states. By plotting the density functions of the QR, the ground-state configuration is found to be a regular polygon.