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Czechoslovak Journal of Physics

Effective charge-spin models for the low energy excitations in quantum dots

Wolfgang Häusler, J. H. Jefferson

Published Apr 1, 1996• 0 citations
Publisher
DOI
10.1007/bf02571194

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It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localized near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin (t-J-V) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods. \textcopyright{} 1996 The American Physical Society.

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Journal of Physics Condensed Matter•May 18, 2001•4 citations
It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localized near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin (t-J-V) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods. \textcopyright{} 1996 The American Physical Society.
We study the spin and charge oscillations of a quantum dot by exactly solving the time-dependent many-body Schr\"odinger equation of a system with a dot embedded in a ring. The dot is characterized by the on-site Coulomb interaction and the gate voltage that governs the occupation status. The itinerant electrons are moving in the ring. By switching on the coupling between the dot and the ring the spin and charge on the dot begin to have undamped oscillations. In the regime of single occupation of the dot, there exists a base frequency of the oscillations that is associated with the spin excitations. Some higher frequencies may be associated with both the charge and spin motions. The results reveal the dynamical characteristics of the spin and charge degrees of freedom and the spectrum of low-energy excitations.
We study the charge and spin currents transported by the elementary excitations of the one-dimensional (1D) Hubbard model and derive the corresponding current spectra. We present results both for finite-size systems and in the thermodynamic limit. This includes finding the couplings of both the low-energy and finite-energy (string) excitations to external charge and spin probes. At zero magnetic field the general structure of the charge-spin separation survives at all energy scales and the effective charges of both the low-energy and finite-energy charge excitations are studied as functions of the on-site Coulomb interaction U , electronic density n , and applied magnetic field H . In some limits the effective charge of the low-energy excitations equals that of the electrons, whereas that of the finite-energy charge-string excitations of rapidity length γ is found to be 2γ times the electronic charge. At U = ∞ the spin excitations do not contribute to spin transport, whereas the low-energy charge excitations feel an effective flux given by (ϕ ↑ N ↑ -ϕ ↓ N ↓ )/( N ↑ + N ↓ ), where N σ is the number of electrons of spin σ and ϕ σ is a spin-dependent flux. This reveals that at zero magnetic field and U = ∞ there is no spin transport, while at finite magnetic field the low-energy charge excitations also carry spin. In the U >> t limit the spin is carried both by holons and spinons. Finally, we find that the charge- and spin-current spectra can be derived from a semi-classical approach.