Nonfreeness and related functionals for measuring correlation in many-fermion states

Gottlieb, Alex D.; Mauser, Norbert J.

doi:10.48550/arxiv.1510.04573

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…The most striking implication is the resulting structural simplification of the N -fermion quantum state. Therefore, studying and understanding (quasi)pinning may provide further insights into concepts as entanglement [25][26][27][28][29] and correlations [30][31][32][33] in few-fermion quantum systems as being recently explored from a quite conceptual and often particularly quantum information theoretical viewpoint.…”

Section: Introductionmentioning

confidence: 99%

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

2016

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The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance of the GPCs is confirmed by analytical means for the ground state in the regime of weak couplings by finding its vector of natural occupation numbers close to the boundary of the allowed region. Such quasipinning is found to become weaker in the intermediate and strong coupling regime. The study of crossovers between different spatial dimensions by detuning the harmonic trap frequencies suggests that quasipinning is essentially an effect for systems with reduced spatial dimensionality. In addition, we find that quasipinning becomes stronger by increasing the degree of spin-polarization. Consequently, the number of states available around the Fermi level plays a key role for the occurrence of quasipinning. This suggests that quasipinning emerges from the conflict between energy minimization and fermionic exchange symmetry.

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Section: Introductionmentioning

confidence: 99%

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

2016

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“…By referring to second quantization, a notion of so-called mode/orbital entanglement and correlation follows naturally, while first quantization leads to the concept of (quantum) nonfreeness. [60][61][62][63]65 The latter quantifies the distance of quantum states to the closest configuration state/Slater determinant. This is also the reason why the nonfreeness provides a promising concise tool for quantifying the intrinsic computational complexity of ground state problems.…”

Section: Discussionmentioning

confidence: 99%

Correlation Paradox of the Dissociation Limit: A Quantum Information Perspective

Ding

Schilling

2020

J. Chem. Theory Comput.

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The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule. While a significant increase of the distance r between the two nuclei marginalizes the electron−electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature T will destroy the entanglement beyond a critical separation distance r crit (T) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.

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“…the 1RDM γ quantifies in terms of the quantum relative entropy S( Γ|| Γ ) ≡ Tr Γ ln( Γ) − ln( Γ ) the 'distance' of a quantum state Γ to the manifold M free of free states [44][45][46][47][48][49][50]. The latter include for fermions (in their closure) the Slater determinants, f † φ1 .…”

Section: Rdmft For Excited States 21 Motivation Of Functional Theoriesmentioning

confidence: 99%

“…Third, by involving the full 1RDM, RDMFT is better suited than DFT for dealing with strongly correlation systems. For instance, according to the nonfreeness [44][45][46][47] for pure states Γ,…”

Section: Rdmft For Excited States 21 Motivation Of Functional Theoriesmentioning

confidence: 99%

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

Liebert

Schilling

2023

New J. Phys.

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Motivated by the Penrose-Onsager criterion for Bose-Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum w and prove a corresponding generalization of the Hohenberg-Kohn theorem: The underlying one-particle reduced density matrix determines all properties of systems of N identical particles in their w-ensemble states. Then, to circumvent the v-representability problem common to functional theories, and to deal with energetic degeneracies, we resort to the Levy-Lieb constrained search formalism in combination with an exact convex relaxation. The corresponding bosonic one-body w-ensemble N-representability problem is solved comprehensively. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli's exclusion principle for fermions and recently discovered generalizations thereof.

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Nonfreeness and related functionals for measuring correlation in many-fermion states

Cited by 3 publications

References 19 publications

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

Correlation Paradox of the Dissociation Limit: A Quantum Information Perspective

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

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