Ladder approximation in coupled quantum-well systems

Yurtsever, Aycan; Tanatar, B.

doi:10.1103/physrevb.63.125320

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…[38], [39], [40]. More specifically, Yurtsever and Tanatar [41] studied coupled quantum wire systems using a perturbation approach based in the ladder approximation of Yasuhara [42].…”

Section: )mentioning

confidence: 99%

Quantum hypernetted chain approximation for one-dimensional fermionic systems

Stoico

Carlevaro

Renzi

et al. 2010

Physica E: Low-dimensional Systems and Nanostructures

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In this comprehensible article we develop, following Fantoni and Rosati formalism, a hypernetted chain approximation for one dimensional systems of fermions. Our scheme differs from previous treatments in the form that the whole set of diagrams is grouped: we do it in terms of nonnodal, non-composite and elementary graphs. This choice makes the deduction of equations more transparent. Equations for the pair distribution functions of one component systems as well as binary mixtures are obtained. We apply they to experimentally realizable quasi-one dimensional systems, the so called quantum wires which we model, within Sommerfeld-Pauli spirit, as a 1D electron gas or as an electron-hole mixture. In order to use our one-dimensional equations we consider pair potentials that depend on the wires width.

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“…[38], [39], [40]. More specifically, Yurtsever and Tanatar [41] studied coupled quantum wire systems using a perturbation approach based in the ladder approximation of Yasuhara [42].…”

Section: )mentioning

confidence: 99%

Quantum hypernetted chain approximation for one-dimensional fermionic systems

Stoico

Carlevaro

Renzi

et al. 2010

Physica E: Low-dimensional Systems and Nanostructures

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“…In fact, investigations in this direction date back long ago, and a great deal of achievement has been made. [13,14,15,16,17,18,19,20,21,22] It is necessary here to give some introduction to the LT. The effective interaction V ef f (p, p ′ ; q) in the LT between two scattering electrons with respective momenta p and p ′ satisfies the following Bethe-Goldstone equation: [23] …”

Section: Introductionmentioning

confidence: 99%

On-top pair-correlation function in the homogeneous electron liquid

Qian

2006

Phys. Rev. B

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The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the shortrange correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density g(0), in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density g(r) at zero distance r = 0.

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Coupled cluster channels in the homogeneous electron gas

Shepherd

Henderson

Scuseria

2014

The Journal of Chemical Physics

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We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.

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Ladder approximation in coupled quantum-well systems

Cited by 3 publications

References 25 publications

Quantum hypernetted chain approximation for one-dimensional fermionic systems

Quantum hypernetted chain approximation for one-dimensional fermionic systems

On-top pair-correlation function in the homogeneous electron liquid

Coupled cluster channels in the homogeneous electron gas

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