�ber die Zahl der Dispersionselektronen, die einem station�ren Zustand zugeordnet sind

Reiche, F.; Thomas, W.

doi:10.1007/bf01328494

Cited by 267 publications

(119 citation statements)

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“…The importance of the continuum states may also be understood by considering the Thomas-Reiche-Kuhn or f -sum rule for an isolated system [18][19][20],…”

Section: Resultsmentioning

confidence: 99%

Self-energy calculation of the hydrogen atom: Importance of the unbound states

Sakuma

Aryasetiawan

2012

Phys. Rev. A

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General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. We present the calculation of the self-energy of the isolated hydrogen atom within the GW approximation starting from the noninteracting Green's function constructed from the exact wave functions of the hydrogen atom. The error in the electron removal energy of the 1s state is found to be about 0.02 eV, which is much smaller than what one would expect. This small error is explained by the cancellation of the self-screening errors between different l contributions of the self-energy. The unbound continuum states are found to be crucial to get the correct self-energy.

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“…The importance of the continuum states may also be understood by considering the Thomas-Reiche-Kuhn or f -sum rule for an isolated system [18][19][20],…”

Section: Resultsmentioning

confidence: 99%

Self-energy calculation of the hydrogen atom: Importance of the unbound states

Sakuma

Aryasetiawan

2012

Phys. Rev. A

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“…(2) allows us to derive a Thomas-Reiche-Kuhn-type [59][60][61] sum rule that may be useful to bound the QFI. Since tanh ω 2T ≤ ω 2T , we have…”

Section: S5 Sum Rulementioning

confidence: 99%

Measuring multipartite entanglement through dynamic susceptibilities

et al. 2016

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Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.Entanglement is a central theoretical concept underlying the characterisation of quantum many-body states in condensed-matter and high-energy physics, as well as quantum information. For example, entanglement properties reveal exotic states of matter such as topological spin liquids [1] or many-body localization [2,3], the holographic entanglement entropy identifies confinement/deconfinement transitions in gauge theories [4,5], and entanglement is considered the central resource for quantum-enhanced metrology [6,7] as well as quantum computation [8][9][10][11]. In experiments, entanglement becomes measurable via a tomographic determination of the many-particle quantum state [12][13][14][15], and protocols have been developed [16] and implemented in remarkable experiments [17] to measure entanglement entropies in quench dynamics and quantum phase transitions. However, the resources required by these protocols scale exponentially with the system size, and these experimental efforts are thus limited a priori to few-particle systems.To address the problem of detecting and quantifying multipartite entanglement for large systems, we consider below the quantum Fisher information (QFI) as an entanglement witness [18][19][20]. Our key result is thatfor a many-body system at thermal equilibrium at any temperature-the QFI can be determined directly from a measurement of Kubo linear response functions, in particular the dynamic susceptibility (see Fig. 1). We emphasise that this measurement prescription is independent of microscopic details of the system of interest and that the measurement of linear response is a standard tool in experiments. Importantly, only modest measurement resources are required that do not scale with system size. The presented prescription therefore makes multipartite entanglement observable for a large variety of * philipp.hauke@uibk.ac.at χ (ω, T ) gives the quantum Fisher information (shaded areas). (c) This pro...

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“…Perhaps the best known sum rule in the atomic theory is the TRK sum rule [4][5][6]. This rule relates the dipole terms zqi between the quantum levels q) and |i) which are coupled by the electric potential field directed along z-axis, namely with the energy differences of the states | q) and |i) given by Let |i) be an initial level and q) is a finite level.…”

Section: Sum Rules For Electron Transitions Between the Atomic Quantumentioning

confidence: 99%

Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

Olszewski

1998

Acta Phys. Pol. A

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A well-known sum rule obtained for electron transitions between the atomic states by Thomas, Reiche and Kuhn (TRK) is examined for the case of transitions between delocalized electron states in cubic lattices. A characteristic point of the original TRK sum rule for the atomic states was its lack of dependence on the initial state of transitions. This situation holds also for the free-electron states in a metal but is changed in the case of electrons influenced by the presence of the field of the crystal core. Corrections to the original TRK result can be represented as a function of the quantum parameter labelling the initial electron state. Other moments of the spectral distribution function than those leading to the TRK sum rule have been calculated. A comparison of the relations found between different spectral moments for solids with similar relations obtained by Traini for the spectral moments of the atomic states has been done.

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�ber die Zahl der Dispersionselektronen, die einem station�ren Zustand zugeordnet sind

Cited by 267 publications

References 0 publications

Self-energy calculation of the hydrogen atom: Importance of the unbound states

Self-energy calculation of the hydrogen atom: Importance of the unbound states

Measuring multipartite entanglement through dynamic susceptibilities

Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

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