Thermodynamics of interacting many-level systems from random-phase-approximation Green's functions

Haley, Stephen B.

doi:10.1103/physrevb.17.337

Cited by 23 publications

(14 citation statements)

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“…For example, Weiss molecular-field calculations show that at absolute zero, I ( I ) I = 3.33 which is some 5% below the saturation value of I = 3.5 (Bowden and Clark 1983). In such cases it may be possible to compute the nuclear statistical tensors using the standard basis operator methods, developed by Haley and Erdos (1972), Bak (1974) and Haley (1978). Alternatively the self-consistent many-body theory of Micnas and Kishore (1980) for standardbasis operator Green functions may be used to good effect.…”

Section: Discussionmentioning

confidence: 99%

“…Thus the simple moment-generating function (exp(aI,)) given by Callen and Shtrikman is no longer valid. Secondly, it is difficult to obtain an RPA expression for the momentgenerating function, because of inconsistencies brought about in the decoupling of higher-order Green functions (see for example Egami and Brooks (1975), Haley and Erdos (1972), Haley (1978)). These arguments suggest therefore, that it might be more rewarding to devise an alternative method of incorporating the quadrupole interaction into the problem, which attempts to maintain the Callen and Shtrikman result for simple ferromagnets.…”

Section: Statistical Tensors and Quadrupole Interactionsmentioning

confidence: 99%

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Spectroscopic investigation of an optically pumped carbon tetrafluoride laser

Alimpiev¹,

Baronov²,

Karlov³

et al. 1979

Sov. J. Quantum Electron.

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The problem of calculating statistical tensors p;(Z) for the nuclear-ordered state in enhanced compounds such as HoVO,, PrNi, etc, is examined within the framework of both a simple effective-field model and more sophisticated many-body theories, such as the RPA. It is shown that for simple ferromagnets and the anti-ferromagnets, a result, originally due to Callen and Shtrikman, can be used to show that there is a one-to-one relationship between the p!$Z) calculated using many-body Green function theories and the simple effective-field model. In addition a new recursion relationship is derived, linking statistical tensors of differing rank. This relationship holds for a wide class of renormalised collective excitation theories and is far more convenient to use in practice than either the momentgenerating function of Callen or the methods of Tahir-Kheli and ter Haar.Using first-order perturbation theory it is also shown that the Callen and Shtrikman result breaks down in the presence of a small axially symmetric quadrupole interaction. Thus it is unlikely that a simple check on the accuracy of 'simple effective-field statistical tensors' can be devised in the spirit of the Callen and Shtrikman result. Some comments are also made concerning the nuclear statistical tensors used to describe the y-ray emission patterns from the enhanced nuclear magnet HoVO, (Allsop er al).

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Section: Discussionmentioning

confidence: 99%

Section: Statistical Tensors and Quadrupole Interactionsmentioning

confidence: 99%

Spectroscopic investigation of an optically pumped carbon tetrafluoride laser

Alimpiev¹,

Baronov²,

Karlov³

et al. 1979

Sov. J. Quantum Electron.

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“…The standard basis operators (SBOs) [31,32] used in I are the excitation operators of the local Hamiltonian h 0 = Un ↑ n ↓ + ǫ d σ n σ . Denoting |µ (µ = 1 ∼ 4) as the eigenstates of h 0 , i.e., h 0 |µ = E µ |µ , we have…”

Section: Second Order V Kσ Expansion Of Gfmentioning

confidence: 99%

Improved strong-coupling perturbation theory of the symmetric Anderson impurity model

Tong

2019

Mod. Phys. Lett. B

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In a previous work (N. H. Tong, Phys. Rev. B 92, 165126 (2015)), an equation-of-motion based series expansion formalism was used to do the second-order strong-coupling expansion for the single-particle Green function of the Anderson impurity model. In this paper, we improve this theory in two aspects. We first use a more accurate scheme to self-consistently calculate the averages that appear in G 1 . In the resummation process, we use updated coefficients for the continued fraction, guided by the formally exact continued fraction from the Mori-Zwanzig theory. These changes lead to more accurate impurity spin response to the magnetic bias of the bath. Combined with the dynamical mean-field theory, our theory gives improved description for the antiferromagnetism of Hubbard model at half filling.

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“…In the following development we shall use as far as possible the notation found in the paper of Haley [5]. We write the Hamiltonian H of a lattice of N identical atoms as follows: fo~~the site i.…”

Section: General Theorymentioning

confidence: 99%

“…A comprehensive formalism for calculating the thermodynamic properties of a solid using random-phase approximation (RPA) Green's functions of standard-basis operators has been recently developed [5]. A comprehensive formalism for calculating the thermodynamic properties of a solid using random-phase approximation (RPA) Green's functions of standard-basis operators has been recently developed [5].…”

mentioning

confidence: 99%