Extended coupled-cluster method. IV. An excitation energy functional and applications to the Lipkin model

Robinson, N. I.; Bishop, R. F.; Arponen, J.

doi:10.1103/physreva.40.4256

Cited by 18 publications

(12 citation statements)

References 55 publications

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“…These features make the Lipkin model an ideal tool for comparing approximate many body theories. 25,[27][28][29][30] Both the variational as well as the traditional coupled cluster approaches are fairly easy to converge.…”

Section: The Lipkin Modelmentioning

confidence: 99%

On the difference between variational and unitary coupled cluster theories

Harsha

Shiozaki

Scuseria

2018

The Journal of Chemical Physics

103

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There have been assertions in the literature that the variational and unitary forms of coupled cluster theory lead to the same energy functional. Numerical evidence from previous authors was inconsistent with this claim, yet the small energy differences found between the two methods and the relatively large number of variational parameters precluded an unequivocal conclusion. Using the Lipkin Hamiltonian, we here present conclusive numerical evidence that the two theories yield different energies. The ambiguities arising from the size of the cluster parameter space are absent in the Lipkin model, particularly when truncating to double excitations. We show that in the symmetry adapted basis under strong correlation, the differences between the variational and unitary models are large, whereas they yield quite similar energies in the weakly correlated regime previously explored. We also provide a qualitative argument rationalizing why these two models cannot be the same. Additionally, we study a generalized non-unitary and non-hermitian variant that contains excitation, de-excitation, and mixed operators with different amplitudes and show that it works best when compared to the traditional, variational, unitary, and extended forms of coupled cluster doubles theories.

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Section: The Lipkin Modelmentioning

confidence: 99%

On the difference between variational and unitary coupled cluster theories

Harsha

Shiozaki

Scuseria

2018

The Journal of Chemical Physics

103

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“…3.5. The overall structure of the ECCM is indicated very schematically in Figure 2, and the interested reader is referred to the literature [67][68][69]90,101,[126][127][128][129][130][131][132] for further details.…”

Section: Formal Elements Of the Extended Ccmmentioning

confidence: 99%

“…2.4 [67,107,129,164]; and the onedimensional Lieb model [86,87] of bosons interacting via repulsive deltafunction potentials [84].…”

mentioning

confidence: 99%

The coupled cluster method

Bishop

Microscopic Quantum Many-Body Theories and Their Applications

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Abstract. The coupled cluster method (CCM) is nowadays widely recognised as providing one of the most powerful, most universally applicable, and numerically most accurate at attainable levels of implementation, of all available ab initio methods of microscopic quantum many-body theory. The number of successful applications of the method to a wide range of physical and chemical systems is impressively large. In almost all such cases the numerical results are either the best or among the best available. A typical example is the electron gas, where the CCM results for the correlation energy agree over the entire metallic density range to within less than one millihartree per electron (or < 1%) with the essentially exact Green's function Monte Carlo results.What has since become known as the normal (NCCM) version of the method was invented some forty years ago to calculate the ground-state energies of closedshell atomic nuclei. Extensions of the CCM have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, stun rules, and the sub-sum-rules that follow from embedding linear response theory within the NCCM. Further extensions deal with the general dynamics of quantum many-body systems, and with their mixed states appropriate, for example, to their behaviour at nonzero temperatures. More recently, a so-called extended (ECCM) version of the method has been introduced. It has the same ability as the NCCM to describe accurately the local properties of quantum many-body systems, but it also has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour.The role of the CCM within modern quantum many-body theory is first surveyed, by a comparison with, and discussion of, the alternative microscopic formulations. We then discuss the method and each of its individual components in considerable detail. Our overall aim is to stress the broad applicability of the method. To that end we introduce and exploit a very general theoretical framework in which to formulate the key ideas and to develop the theory. We end with a brief review of the applications of the method to date.

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“…The extended exp(S)-formalism tries to resolve the problem by an improved model for (~1 = (~l e s+ which still allows to work with eS-transformed operators, similar as in (14) [22,24,25] 9 To this end one introduces a complementing n-hole, n-particle correlation operator S' as s' =ys. which again has the desirable feature that it terminates at finite order for a given n-body operator A.…”

Section: The Extended Exp(s) Ansatzmentioning

confidence: 99%

“…In Sect. 3 we shortly review the extended exp(S) formalism of Arponen et al [22][23][24][25] and present the equations of motion for time-dependent correlations in this framework. Necessary technical approximations introduce non-unitary components in the propagation of the amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Truncation of time-dependent many-body theories

Schmitt

Reinhard

Toepffer

1990

Z. Physik A - Atomic Nuclei

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We investigate truncation schemes for the many-body dynamics of finite fermion systems beyond the time-dependent Hartree-Fock (TDHF) approximation. One approach starts from the quantum Bogolyubov-BornGreen-Kirkwood-Yvon (BBGKY-)hierarchy of equations of motion for density matrices. It is shown that simple truncation of higher correlations within this scheme is inconsistent because essential exchange correlations are lost. As an alternative, we study the (extended) exp(S) or coupled-cluster formalism. It provides a wider range of applicability. But it also runs into problems with non-unitary propagation after truncation.

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Extended coupled-cluster method. IV. An excitation energy functional and applications to the Lipkin model

Cited by 18 publications

References 55 publications

On the difference between variational and unitary coupled cluster theories

On the difference between variational and unitary coupled cluster theories

The coupled cluster method

Truncation of time-dependent many-body theories

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