Unrestricted Hartree-Fock for Quantum Dots

Boris Reusch; Hermann Grabert

RECORD

Unrestricted Hartree-Fock for Quantum Dots

Boris Reusch, Hermann Grabert

Strongly Correlated Electrons · Submitted 27 May 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,153 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.80 · human participants 0.01 · controlled comparison 0.65 · randomized assignment 0.01 · states quantitative result 0.35 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present detailed results of Unrestricted Hartree-Fock (UHF) calculations for up to eight electrons in a parabolic quantum dot. The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features. To elucidate the significance of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF) and UHF. While UHF symmetry breaking admits lower ground-state energies, misconceptions in the interpretation of UHF densities are pointed out. An analysis of the orbital energies shows that for very strong interaction the UHF Hamiltonian is equivalent to a tight-binding Hamiltonian. This explains why the UHF energies become nearly spin independent in this regime while the RHF energies do not. The UHF densities display an even-odd effect which is related to the angular momentum of the Wigner molecule. In a weak transversal magnetic field this even-odd effect disappears.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present detailed results of Unrestricted Hartree-Fock (UHF) calculations for up to eight electrons in a parabolic quantum dot.	contribution 0.99	0.97	0.08	asserted 0.97
s1	The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features.	result 0.99	0.92	0.64	asserted 0.98
s2	To elucidate the significance of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF) and UHF.	method 0.80	0.85	0.04	asserted 0.68
s3	While UHF symmetry breaking admits lower ground-state energies, misconceptions in the interpretation of UHF densities are pointed out.	interpretation 0.59	0.83	0.13	asserted 1.00
s4	An analysis of the orbital energies shows that for very strong interaction the UHF Hamiltonian is equivalent to a tight-binding Hamiltonian.	result 0.66	0.89	0.09	asserted 1.00
s5	This explains why the UHF energies become nearly spin independent in this regime while the RHF energies do not.	interpretation 0.97	0.84	0.11	asserted 1.00
s6	The UHF densities display an even-odd effect which is related to the angular momentum of the Wigner molecule.	result 0.92	0.92	0.09	asserted 1.00
s7	In a weak transversal magnetic field this even-odd effect disappears.	result 1.00	0.83	0.05	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.99 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We present detailed results of Unrestricted Hartree-Fock (UHF) calculations for up to eight electrons in a parabolic quantum dot. The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features. To elucidate the significance of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF) and UHF. While UHF symmetry breaking admits lower ground-state energies, misconceptions in the interpretation of UHF densities are pointed out. An analysis of the orbital energies shows that for very strong interaction the UHF Hamiltonian is equivalent to a tight-binding Hamiltonian. This explains why the UHF energies become nearly spin independent in this regime while the RHF energies do not. The UHF densities display an even-odd effect which is related to the angular momentum of the Wigner molecule. In a weak transversal magnetic field this even-odd effect disappears.

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