Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems

Arponen, J.

doi:10.1016/0003-4916(83)90284-1

Cited by 412 publications

(390 citation statements)

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“…Our analysis extends the well-established coupled-cluster method (CCM) [3,4,5] to a variational formalism in which bra and ket states are now hermitian to one another, contrast to the traditional CCM where they are not [6]. Ever since the CCM was first proposed, attempts have been made to extend it to a standard variational formalism, for examples, in the seventies in nuclear physics [7] and later in quantum chemistry [8].…”

Section: Introductionmentioning

confidence: 95%

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

Xian¹

2007

J. Phys.: Condens. Matter

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We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin ±1. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.

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Section: Introductionmentioning

confidence: 95%

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

Xian¹

2007

J. Phys.: Condens. Matter

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“…A brief description of the normal coupled cluster method (NCCM) formalism is now provided, although the interested reader is referred to [16][17][18][19][20][21][22][23][24]. for further details.…”

Section: The Ccl'vi Formalismmentioning

confidence: 99%

“…}'oremost among the most versatile technique:o in the modern arsenal of QMBT arc tho::;e such as quantum Monte Carlo (Q"lC) methods [1][2][3][4] the correlated basis function (CBF) method [5 15] and the coupled clu::;(er method (CCM) [16][17][18][19][20][21][22][23][24], on the la::;t of which we concentrate in this Chapter.…”

Section: Introductionmentioning

confidence: 99%

The coupled cluster method applied to quantum magnetism

Farnell

Bishop

2004

Lecture Notes in Physics

121

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Abstract. The Coupled Cluster Method (CC\I) is one of the most powerful and universally applied techniques of quanturn many-body theory. In particular, it has been used extensively in order to investigate many types of lattice quantum spin system at zero temperature. The ground-and excited-state properties of these systerns may now be determined routinely to great accuracy. In this Chapter we present an overview of the CCM formalism and we describe how the CC1\1 is applied in detaiL \Ve illustrate the power and versatility of the method by presenting results for four diH'erent spin models. These are, namely, the XXZ model, a Heisenberg model with bonds of differing strengths on the square lattice. a model which interpolates between the Kagome-and triangular-lattice antiferromagnets. and a frustrated ferrimagnetic spin system on the square lattice. vVe consider the ground-state properties of all of these systems and we present accurate results for the excitation energies of the spin-half square-lattice XXZ model. vVe utilise an "extcnded" SUB2 approximation scheme. and we demonstrate how this approximation Illay be solved exactly by using Fourier transform methods or, alternatively, by determining and solving the SUB2-m problem. \Ve also present the rcsults of "localised" approximation schemes called the LSUBm or SUBm-m schemes. \Ve note t hat we must utilise computational techniques in order to solvc these localised approximation schemes to "high order" vVe show that we are able to determine the positions of quantum phase transitions with much accuracy, and we demonstrate that we are able to determine their quantum criticality by using the CClvi in conjunction with the coherent anomaly method (CAM). Also. we illustrate that the CCM lnay be used in order to determine the "nodal surfaces" of lattice quantum spin systems, Finally. we show how connections to cumulant series expansions ma:-' be made by determining the perturbation series of a spin-half triangular-lattice antiferromagnet using the CCM at various levels of LSUBm approximation, IntroductionKey experimental observations in fields such as supcrfluidity, superconductivity, nuclear structure, quantum chemistry, quantum magnetism and strOllgly correlated electronic systems have often implied that the strong quantum correlations inherent in these systems should be fully included, at least conceptually, in any theoretical calculations that aim fully to describe their basic

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“…"Alternative" CC methods have been proposed, including extended coupled cluster 34 (ECC), quadratic coupled cluster 35 (QCC), improved coupled cluster 36 (ICC), unitary coupled cluster [37][38][39][40] (UCC), and variational coupled cluster 41 (VCC), and a number of studies 20,[28][29][30][31][32][33] have confirmed the superiority of VCC and related approaches over TCC for the treatment of problems involving strong static correlation. This can be attributed to the upper bound property of VCC, which ensures that calculated VCC energies are always higher than FCI energies, which is not the case for TCC.…”

Section: Introductionmentioning

confidence: 99%

Quasi-variational coupled cluster theory

Robinson

Knowles

2012

The Journal of Chemical Physics

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Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface for high-temperature applications JCP: BioChem. Phys. 6, 01B616 (2012) Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface for high-temperature applications J. Chem. Phys. 136, 044320 (2012) A theoretical study of the CX2N radicals (X = F, Cl, Br): The effect of halogen substitution on structure, isomerization, and energetics J. Chem. Phys. 136, 044316 (2012) Molecular properties via a subsystem density functional theory formulation: A common framework for electronic embedding J. Chem. Phys. 136, 044104 (2012) Statistical thermodynamics of 1-butanol, 2-methyl-1-propanol, and butanal J. Chem. Phys. 136, 034306 (2012) Additional information on J. Chem. Phys. We extend our previous work on the construction of new approximations of the variational coupled cluster method. By combining several linked pair functional transformations in such a way as to give appropriately balanced infinite-order contributions, in order to approximate eT †Ĥ eT L well at all orders, we formulate a new quantum chemical method, which we name quasi-variational coupled cluster. We demonstrate this method to be particularly robust in the regime of strong static electron correlation, improving significantly on our earlier approximate variational coupled cluster approach.

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Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems

Cited by 412 publications

References 31 publications

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

The coupled cluster method applied to quantum magnetism

Quasi-variational coupled cluster theory

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