Functional theory for Bose-Einstein condensates

Liebert, Julia; Schilling, Christian

doi:10.1103/physrevresearch.3.013282

Cited by 13 publications

(26 citation statements)

References 45 publications

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“…The application of w-ensemble RDMFT to Bose-Einstein condensates (BECs) is appealing due to a number of reasons. First, as already stressed in the introduction the Penrose and Onsager criterion [14,16] for BEC identifies RDMFT as a particularly suitable approach to BECs. Second, recent analyses of their ground states have revealed an intriguing new concept, namely the existence of a BEC-force [15,16,56].…”

Section: Application To Bose-einstein Condensatesmentioning

confidence: 94%

“…First, as already stressed in the introduction the Penrose and Onsager criterion [14,16] for BEC identifies RDMFT as a particularly suitable approach to BECs. Second, recent analyses of their ground states have revealed an intriguing new concept, namely the existence of a BEC-force [15,16,56]. The question arises whether this force based on the one-particle picture is also present in excited BECs.…”

Section: Application To Bose-einstein Condensatesmentioning

confidence: 94%

“…The importance of the constrained search expression (16) of the relaxed w-ensemble functional F w can hardly be overestimated. It will namely serve as the starting point for the construction of functional approximations.…”

Section: B Convex Relaxation Of W-ensemble Rdmftmentioning

confidence: 99%

“…The calculation shown in the following uses the same concepts as in Ref. [16] but derives F w0 as a functional of η rather than of the full occupation number vector n.…”

Section: A Recap Of Ground State Universal Functionalmentioning

confidence: 99%

“…Actually, its scope would even extend to arbitrary strongly correlated bosonic quantum systems since the 1RDM provides direct insights into the correlation strength through its degree of mixedness. Despite all these points, the foundation for a bosonic ground state RDMFT was proposed only very recently [15,16]. This is even more remarkable, since its fermionic counter part is enjoying an intensive ongoing development .…”

Section: Introductionmentioning

confidence: 99%

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An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability

Liebert¹,

Schilling²

2022

Preprint

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We propose, work out and initiate a one-particle reduced density matrix functional theory (RDMFT) for targeting excitation energies of bosonic quantum systems. In analogy to its recently established fermionic counterpart, this bosonic w-ensemble RDMFT is based on a generalization of the Rayleigh-Ritz variational principle to ensemble states with spectrum w used within the constrained search formalism. Most importantly, an exact convex relaxation is implemented to turn w-ensemble RDMFT into a practically feasibly method: The corresponding convex-relaxed 1-body w-ensemble N -representability problem can be solved, revealing a complete hierarchy of exclusion principle constraints in analogy to Pauli's famous principle for fermions. To initiate w-ensemble RDMFT, we systematically derive universal functionals for the symmetric Bose-Hubbard dimer and for Bose-Einstein condensates in the Bogoliubov regime.

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Section: Application To Bose-einstein Condensatesmentioning

confidence: 94%

Section: Application To Bose-einstein Condensatesmentioning

confidence: 94%

Section: B Convex Relaxation Of W-ensemble Rdmftmentioning

confidence: 99%

“…The calculation shown in the following uses the same concepts as in Ref. [16] but derives F w0 as a functional of η rather than of the full occupation number vector n.…”

Section: A Recap Of Ground State Universal Functionalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability

Liebert¹,

Schilling²

2022

Preprint

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Advances in approximate natural orbital functionals: From historical perspectives to contemporary developments

Piris

2024

Advances in Quantum Chemistry

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Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

Lew-Yee

Campo

Piris

2022

J. Chem. Theory Comput.

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The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via secondorder Møller−Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.

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Functional theory for Bose-Einstein condensates

Cited by 13 publications

References 45 publications

An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability

An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability

Advances in approximate natural orbital functionals: From historical perspectives to contemporary developments

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

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