Density functionals and model Hamiltonians: Pillars of many-particle physics

Capelle, K.; Campo, Vivaldo L.

doi:10.1016/j.physrep.2013.03.002

Cited by 96 publications

(134 citation statements)

References 291 publications

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“…We have derived some exact expressions for the two-electron ground state wavefunction and its associated electronic density. We hope that this atomic model is useful for future work on fundamental issues such as entanglement and Fisher-Shannon information, as well as being a theoretical laboratory to test concepts and approximations in density functional theory and other numerical methodologies [49]. Finally, we note that the artificial atom described in this work also leads to analytical solutions in lower dimensions.…”

Section: Discussionmentioning

confidence: 79%

Two-electron atom with a screened interaction

Downing

2017

Phys. Rev. A

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We present analytical solutions to a quantum mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced by harmonic potentials. The electron-electron interaction potential is taken to be both screened (decaying faster than the inverse of the interparticle separation) and regularized (in the limit of zero separation). We reveal the exactly solvable few-electron ground-state, which explicitly includes electron correlation, for certain values of the harmonic containment.

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Section: Discussionmentioning

confidence: 79%

Two-electron atom with a screened interaction

Downing

2017

Phys. Rev. A

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“…As we want to reformulate DFT in the orbital space, orbitals occupation {n i } i seems to be the variable of choice. This is known in condensed matter physics as Site-Occupation Functional Theory (SOFT) [14,33,34]. The latter is nothing but the formulation of DFT for model Hamiltonians such as the Hubbard Hamiltonian.…”

Section: Dft For Model Hamiltoniansmentioning

confidence: 99%

“…The latter expression is usually referred to as the Hartree energy in condensed matter physics [14]. The exchange energy is then considered to be zero.…”

Section: Soft and Its Ks Formulationmentioning

confidence: 99%

“…As a major difference with the approaches discussed previously, orbitals occupation will be used as basic variable rather than the electron density. The idea originates from condensed matter physics where strongly correlated electrons are usually described with model Hamiltonians (such as the Hubbard Hamiltonian) rather than the true physical one [14]. As discussed further in the following, adapting such an approach to quantum chemistry is appealing since static correlation is usually defined in the orbital space.…”

Section: Introductionmentioning

confidence: 99%

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On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

Fromager

2015

Molecular Physics

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The exact formulation of multi-configuration density-functional theory (DFT) is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of Configuration Interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact Site-Occupation Embedding Theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with Density Matrix Embedding Theory (DMET) is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact Complete Active Space Site-Occupation Functional Theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described with an orbital occupation functional. The computational implementation of SOET and CASSOFT as well as the development of approximate functionals are left for future work.

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“…To improve efficiency of modelling and prediction power it is now possible p-1 to use approximations in DFT to efficiently model lattice systems (see, e.g., Ref. 21 and references therein).…”

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confidence: 99%

Uniqueness of density-to-potential mapping for fermionic lattice systems

Coe¹,

D’Amico²,

França³

2015

EPL

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PACS 31.15.ec -Hohenberg-Kohn theorem and formal mathematical properties, completeness theorems PACS 71.10.Fd -Lattice fermion models (Hubbard model, etc.) PACS 71.15.Mb -Density functional theory, local density approximation, gradient and other correctionsAbstract -We demonstrate that, for a fermionic lattice system, the ground-state particle density uniquely determines the external potential except for the sites corresponding to nodes of the wave function, and the limiting case where the Pauli exclusion principle completely determines the occupation of all sites. Our fundamental finding completes, for this general class of systems, the one-to-one correspondence between ground states, their densities, and the external potential at the base of the Hohenberg-Kohn theorem. Moreover we demonstrate that the mapping from wave function to potential is unique not just for the ground state, but also for excited states. To illustrate our findings, we develop a practical inversion scheme to determine the external potential from a given density. Our results hold for a general class of lattice models, which includes the Hubbard model.Mapping many-body systems to a lattice while neglecting interactions beyond a given order has proven a powerful aid to devise tractable models -such as the Hubbard [1] and Heisenberg (see, e.g., Ref.[2]) models -and further the understanding of their properties. Lattice systems are of recent interest for quantum chemistry calculations when the one-particle wave functions can be appropriately mapped to sites in a one-dimensional lattice and DMRG techniques are used to model the system (see, e.g., Refs. 3-5). In addition, lattice systems, both bosonic and fermionic, may be simulated experimentally using an optical lattice (see, e.g., Refs. 6-8). The latter is of great interest to the quantum technology community for developing quantum simulators. Fermionic lattice systems have been used to model the entanglement of nanostructures [9] and, using time-dependent density-functional theory, have been employed to investigate the time evolution of the out-ofequilibrium Mott insulator [10]. Time-dependent densityfunctional theory has also been used to create a method to simulate driven lattice gases with interactions [11] and used with other classical lattice Hamiltonians to model particle transport against a bias [12]. Lattice Hamiltonians have been used to describe the process of excitationenergy transfer and the role of intramolecular vibrations in the photosynthetic process [13]. Lattice systems are also used to simulate molecular systems, as for example the Pariser-Parr-Pople (PPP) model [14,15], similar to the inhomogeneous Hubbard model, can describe molecular systems with delocalised electrons in π-orbitals and has recently been used to model armchair polyacenes in Ref. 16. In the last decades density-functional theory (DFT) [17] in all its flavors has been a very important tool to predict properties of materials and structures. DFT is in principle an exact theory and allows to map many-body p...

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Density functionals and model Hamiltonians: Pillars of many-particle physics

Cited by 96 publications

References 291 publications

Two-electron atom with a screened interaction

Two-electron atom with a screened interaction

On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

Uniqueness of density-to-potential mapping for fermionic lattice systems

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