Ensemble Reduced Density Matrix Functional Theory for Excited States and Hierarchical Generalization of Pauli’s Exclusion Principle

Schilling, Christian; Pittalis, Stefano

doi:10.1103/physrevlett.127.023001

Cited by 33 publications

(43 citation statements)

References 62 publications

(91 reference statements)

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“…The spectra of operators in D 1 N (w) retain a physical relevance to study 1-particle reduced density matrix functional theory for excited states, see [SP21][LCLS21] and Section 2.4. This description refines and solves a constrained 1-body N -representability problem, where the weights of the ensemble can be specified [AK08, Theorem 3].…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…Convexity Ansatz. The present article draws its motivation from this practical consideration, and the notion of convexity plays a key role: Convexity is essential in the foundation of reduced density matrix functional theory for excited states [SP21] [LCLS21]. Herein, we provide an effective solution to a convex relaxation of the constrained 1-body N -representability problem on which reduced density matrix functional theory relies, see Figure 6.…”

Section: No-win Scenario For Coulson's Vision? Unfortunately Although...mentioning

confidence: 99%

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An effective solution to convex $1$-body $N$-representability

Castillo¹,

Labbé²,

Liebert³

et al. 2021

Preprint

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From a geometric point of view, Pauli's exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of 1-fermion and N -fermion density matrices, therefore it coincides with the convex hull of the pure N -representable 1-fermion density matrices. Consequently, the description of ground state physics through 1-fermion density matrices may not necessitate the intricate pure state generalized Pauli constraints. In this article, we study the generalization of the 1-body N -representability problem to ensemble states with fixed spectrum w, in order to describe finite-temperature states and distinctive mixtures of excited states. By employing ideas from convex analysis and combinatorics, we present a comprehensive solution to the corresponding convex relaxation, thus circumventing the complexity of generalized Pauli constraints. In particular, we adapt and further develop tools such as symmetric polytopes, sweep polytopes, and Gale order. For both fermions and bosons, generalized exclusion principles are discovered, which we determine for any number of particles and dimension of the 1-particle Hilbert space. These exclusion principles are expressed as linear inequalities satisfying hierarchies determined by the non-zero entries of w. The two families of polytopes resulting from these inequalities are part of the new class of so-called lineup polytopes.

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Section: Summary Of Resultsmentioning

confidence: 99%

Section: No-win Scenario For Coulson's Vision? Unfortunately Although...mentioning

confidence: 99%

An effective solution to convex $1$-body $N$-representability

Castillo¹,

Labbé²,

Liebert³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…How to cite this article: J. Jara-Cortés, C. F. 68,69 Several conditions such as N-representability, hermiticity, antisymmetry and the the sum rule between the 1-RDM and 2-RDM, among others, should be complied by the approximations.…”

Section: Data Availability Statementmentioning

confidence: 99%

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states

2022

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An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact V xc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.excited states, atomic energies, chromophore, interacting quantum atoms (IQA), quantum theory of atoms in molecules (QTAIM) | INTRODUCTIONEnergy drives chemistry, reactivity, and photophysical properties of matter. Spectroscopy at its core is a study of energy changes accompanying transitions between quantum states, namely, excitations and de-excitations. These transitions can be among rotational, vibrational, or electronic levels-or combinations of these levels, as is well-known. This work focuses on energy changes due to a change in molecular electronic state manifested in UV/Vis spectra.A core concept of spectroscopy is that of the chromophore. Spectroscopists ascribe characteristic "fingerprints" to different functional groups, that is, a set of consistent and relatively constant absorption or emission features that characterize a particular functional group irrespective of the molecule where it exists. This quasi-constancy of properties (the spectroscopic fingerprint being just one example of which) is what theorists and experimentalists who study molecular charge densities in real space term "transferability" [see for example References 1-15].

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“…A corresponding extended RDMFT was introduced for fermions in Ref. [38,39], as a generalization of the well-known DFT for excited states (GOK-DFT) [40][41][42]. The bosonic counterpart of this so-called w-ensemble RDMFT is missing so far.…”

Section: Introductionmentioning

confidence: 99%

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

Liebert¹,

Schilling²

2022

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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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Ensemble Reduced Density Matrix Functional Theory for Excited States and Hierarchical Generalization of Pauli’s Exclusion Principle

Cited by 33 publications

References 62 publications

An effective solution to convex $1$-body $N$-representability

An effective solution to convex $1$-body $N$-representability

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states

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

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