t-Matrix perturbation theory of solid helium

Brandow, B.H.

doi:10.1016/0003-4916(72)90262-x

Cited by 49 publications

(4 citation statements)

References 132 publications

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“…Calculations were carried out directly within the Wannier basis appropriate for the assigned magnetic sublattices; the noncanonical equations (1) and (2) were solved iteratively by an extension of techniques described in [22]. Figure 1 shows the Wannier orbitals of a self-consistent solution for a seven-site unit cell with the assigned spin configuration 1.1 t t t i t .…”

Section: Local Moment Hartree-fock Theorymentioning

confidence: 99%

“…To do this, we have constructed a one-dimensional model system [22] for which the nonlocality of the exchange potential can be treated exactly by standard numerical methods. The system consists of an infinite row of "one-dimensional hydrogen atoms," with a Coulomb-like interaction which is rounded off near the origin, and cut off in a smooth but rapid manner at large distances,…”

Section: Local Moment Hartree-fock Theorymentioning

confidence: 99%

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Theory of mott insulators

Brandow

2009

Int. J. Quantum Chem.

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The main characteristics of Mott insulator materials are qualitatively explained by means of a suitable form of Hartree-Fock approximation. This can be regarded as an extension of the Slater antiferromagnetic band theory. Semiquantitative applications to NiO and COO are described. The aspects discussed include the insulating gap, origin of the antiferromagnetic spin coupling, reasons for the validity of the crystal-field model, 3d bandwidth questions, and a survey of the basic microscopic mechanisms responsible for related insulatormetal transitions.

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Section: Local Moment Hartree-fock Theorymentioning

confidence: 99%

Section: Local Moment Hartree-fock Theorymentioning

confidence: 99%

Theory of mott insulators

Brandow

2009

Int. J. Quantum Chem.

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“…where typically A -0.1 and L = 4.0 lattice units. Calculations were carried out directly within the Wannier basis appropriate for the assigned magnetic sublattices; the noncanonical equations (1) and (2) were solved iteratively by an extension of techniques described in [22]. Figure 1 shows the Wannier orbitals of a self-consistent solution for a seven-site unit cell with the assigned spin configuration 1.1 t t t i t .…”

Section: Local Moment Hartree-fock Theorymentioning

confidence: 99%

Theory of Mott Insulators

Brandow¹

1988

NATO ASI Series

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“…This is done by using several different approaches: we have theories basing on diagrammatical methods arriving at the reduction by summing up special classes of diagrams. [1][2][3][4] Other methods are in some aspects intuitive and "'phenomenologmal". 5 6 Their authors invent a model two-particle problem as a starting point for their calculations.…”

Section: Introductionmentioning

confidence: 99%

The self-energy problem in ground state and phonon calculation of quantum solids

Bolterauer

Gillessen

1976

J Low Temp Phys

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What part self-energy plays in T-matrix theories for quantum crystals has not yet been entirely understood. 1t7 particular, quantities related to the self-energy (e.g., the single-particle potential and the T matrix as an effective interaction extracted from the ground-state theory) have been used in phonon calculations in an uncritical fashion. In order to have a common basis for the comparison of the existing theories, we have diagrammatically reformulated the theories of Iwamoto and Namaizawa and of Guyer and Zane respectively. We then show what kind of approximations have been made in the existing theories concerning the single-particle potential and the effective interaction. Using the self-energy we propose an improved method to determine these quantities which enables us to treat phonon and ground-state calculations on an equal footing. Additionally, we set up a diagrammatic two-particle approximation method, which can be used in ground-state theory, and in phonon calculations as well. Contrm3' to the existing theories not referring to the self-energy, our procedure remains consistent, transferring the ground-state effective interaction to the phonon calculation. We show for example, that a suitably chosen effective interaction can be used as a renormalized interaction in an RPA calculation without overcounting any diagrams.

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t-Matrix perturbation theory of solid helium

Cited by 49 publications

References 132 publications

Theory of mott insulators

Theory of mott insulators

Theory of Mott Insulators

The self-energy problem in ground state and phonon calculation of quantum solids

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