Configuration interaction method for Fock–Darwin states

Wensauer, Andreas; Korkusiński, Marek; Hawrylak, Paweł

doi:10.1016/j.ssc.2003.12.039

Cited by 30 publications

(33 citation statements)

References 49 publications

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“…Donor positions are assigned at evenly spaced (R 0 ) substitutional atomic sites in Si along a [110] crystalline direction. The many-body state is described within the Configuration Interaction (CI) framework [17][18][19][20] and diagonalized exactly. Since Si is a material with very low spin-orbit coupling and no piezoelectric phonons, it is reasonable to assume that spin relaxation times are much longer than all other time scales involved in the experiment, so that thermalization does not remove the system from the S z = 0 subspace.…”

Section: Resultsmentioning

confidence: 99%

Adequacy of Si:P chains as Fermi–Hubbard simulators

et al. 2018

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The challenge of simulating many-body models with analogue physical systems requires both experimental precision and very low operational temperatures. Atomically precise placement of dopants in Si permits the construction of nanowires by design. We investigate the suitability of these interacting electron systems as simulators of a fermionic extended Hubbard model on demand. We describe the single-particle wavefunctions as a linear combination of dopant orbitals (LCDO). The electronic states are calculated within configuration interaction (CI). Due to the peculiar oscillatory behavior of each basis orbital, properties of these chains are strongly affected by the interdonor distance R 0 , in a non-monotonic way. Ground state (T = 0 K) properties such as charge and spin correlations are shown to remain robust under temperatures up to 4 K for specific values of R 0 . The robustness of the model against disorder is also tested, allowing some fluctuation of the placement site around the target position. We suggest that finite donor chains in Si may serve as an analog simulator for strongly correlated model Hamiltonians. This simulator is, in many ways, complementary to those based on cold atoms in optical lattices-the trade-off between the tunability achievable in the latter and the survival of correlation at higher operation temperatures for the former suggests that both technologies are applicable for different regimes.

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Section: Resultsmentioning

confidence: 99%

Adequacy of Si:P chains as Fermi–Hubbard simulators

et al. 2018

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“…We comment that modeling the quantum dot geometry by a perturbed harmonic oscillator is justified by selfconsistent calculations [13][14][15] and is a widely adopted assumption. 5,8,9,[16][17][18] The Hamiltonian of the quantum dot is given by…”

Section: B Parabolic Quantum Dotsmentioning

confidence: 99%

“…We demonstrate the estimates with calculations in the d = 2 dimensional case for N Յ 5 electrons, paralleling computations in the literature. [5][6][7][8][9][10] The main results are however somewhat discouraging. The expansion coefficients of typical eigenfunctions are shown to decay very slowly, limiting the accuracy of any practical method using HO basis functions.…”

Section: Introductionmentioning

confidence: 97%

Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

Kvaal

2009

Phys. Rev. B

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We give a thorough analysis of the convergence properties of the configuration-interaction method as applied to parabolic quantum dots among other systems, including a priori error estimates. The method converges slowly in general, and in order to overcome this, we propose to use an effective two-body interaction well known from nuclear physics. Through numerical experiments we demonstrate a significant increase in accuracy of the configuration-interaction method.

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“…The energy spectrum of an interacting two-electron NWQD is calculated using the standard numerical exact diagonalization technique [8]. The numerically exact results are obtained by increasing the numbers of chosen single electron orbital basis and the corresponding two-electron configurations until a numerical convergence is achieved.…”

Section: Exact Diagonalizationmentioning

confidence: 99%

Singlet–triplet transitions in highly correlated nanowire quantum dots

Chen

Chao

Huang

et al. 2010

Physica E: Low-dimensional Systems and Nanostructures

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We consider a quantum dot embedded in a three-dimensional nanowire with tunable aspect ratio a. A configuration interaction theory is developed to calculate the energy spectra of the finite 1D quantum dot systems charged with two electrons in the presence of magnetic fields B along the wire axis. Fruitful singlet-triplet transition behaviors are revealed and explained in terms of the competing exchange interaction, correlation interaction, and spin Zeeman energy. In the high aspect ratio regime, the singlet-triplet transitions are shown designable by tuning the parameters a and B. The transitions also manifest the highly correlated nature of long nanowire quantum dots.

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Configuration interaction method for Fock–Darwin states

Cited by 30 publications

References 49 publications

Adequacy of Si:P chains as Fermi–Hubbard simulators

Adequacy of Si:P chains as Fermi–Hubbard simulators

Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

Singlet–triplet transitions in highly correlated nanowire quantum dots

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