An efficient method for strongly correlated electrons in one dimension

Mitxelena, Ion; Piris, Mario

doi:10.1088/1361-648x/ab6d11

Cited by 24 publications

(18 citation statements)

References 31 publications

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“…These interactions may produce significant differences between both model systems. Recently [36], we have proven the ability of PNOF7 to describe the symmetric and asymmetric dissociations of a 1D hydrogen chain with 50 atoms, wherein the PNOF7 energies compared remarkably well with those obtained at the DMRG level of theory along the dissociation curves. The addition of a spatial dimension increases the amount of interactions and makes the bond-breaking process more complex, so new and diverse strong correlations can emerge.…”

Section: Two-dimensional Hydrogen Latticementioning

confidence: 64%

An efficient method for strongly correlated electrons in two-dimensions

Mitxelena

Piris

2020

The Journal of Chemical Physics

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This work deals with the problem of strongly correlated electrons in two-dimensions (2D). We give a reduced density matrix (RDM) based tool through which the ground-state energy is given as a functional of the natural orbitals and their occupation numbers. Specifically, the Piris Natural Orbital Functional 7 (PNOF7) is used for studying the 2D Hubbard model and hydrogen square lattices. The singlet ground-state is studied, as well as the doublet mixed quantum state obtained by extracting an electron from the system. Our method satisfies two-index necessary N-representability conditions of the two-particle RDM (2RDM) and guarantees the conservation of the total spin. We show the ability of PNOF7 to describe strong correlation effects in 2D systems by comparing our results with exact diagonalization, density matrix renormalization group (DMRG), and auxiliaryfield quantum Monte Carlo calculations. PNOF7 overcomes variational 2RDM methods with twoand three-index positivity N-representability conditions, reducing computational cost to mean-field scaling. Consistent results are obtained for small and large systems up to 144 electrons, weak and strong correlation regimes, and many filling situations. Unlike other methods, there is no dependence on dimensionality in the results obtained with PNOF7, and no particular difficulties have been observed to converge PNOF7 away from half-filling. Smooth double occupancy of sites is obtained regardless of the filling. Symmetric dissociation of 2D hydrogen lattices shows that long-range nondynamic correlation drammatically affects electron detachment energies. PNOF7 compares well with DMRG along the dissociation curve.

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Section: Two-dimensional Hydrogen Latticementioning

confidence: 64%

An efficient method for strongly correlated electrons in two-dimensions

Mitxelena

Piris

2020

The Journal of Chemical Physics

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“…40,41,[118][119][120][121][122][123][124][125][126][127][128][129] Variational APSG is equivalent to the Piris natural orbital functional PNOF5, 130,131 meaning that the APSG 2-RDM is expressible directly in terms of its 1-RDM elements. Recently, the PNOF7 functional [132][133][134][135][136][137] has shown convincing numerical results. In its simplest form PNOF7 is based on closed-shell pairs (generalizations are possible and pointed out in ref 132 ), but the intra-pair and inter-pair interactions are treated separately.…”

Section: Apsg: Sparsitymentioning

confidence: 99%

Density Matrices of Seniority-Zero Geminal Wavefunctions

Moisset,

Fecteau,

Johnson

2022

Preprint

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Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analogue of Wick's theorem for fermions or bosons. This expression is in general intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly-orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals.Both are near exact suggesting that the incorrect results observed with ground state RG states are fixable using a different RG state.

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“…The lack of intersubspace interaction in PNOF5 lead to the later versions of PNOFx functionals (like PNOF7). The PNOF7 functional accounts for the interaction among pairs and has been proven account for the so-called nondynamic correlation energy, but it misses the dynamic one [34,35,103]. In an attempt to account for both types of electron correlation the GNOF functional was recently proposed [106]; it has proven to be capable of accounting for an important part of the so-called dynamic correlation energy.…”

Section: Approximations Built Imposing N -Representability Conditionsmentioning

confidence: 99%

“…RDMFT is emerging as a strong competitor to the widely used density functional theory (DFT) due to the possibility to use fractional occupation numbers, which facilitates the study of electronic systems where the socalled nondynamic correlation effects are enhanced [29][30][31][32][33][34][35]. Indeed, the popular working horse of physicists and chemists (i.e.…”

Section: Introductionmentioning

confidence: 99%

Relativistic reduced density matrix functional theory

Rodríguez-Mayorga¹,

Giesbertz²,

Visscher³

2022

Preprint

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As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the firstorder reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties.

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An efficient method for strongly correlated electrons in one dimension

Cited by 24 publications

References 31 publications

An efficient method for strongly correlated electrons in two-dimensions

An efficient method for strongly correlated electrons in two-dimensions

Density Matrices of Seniority-Zero Geminal Wavefunctions

Relativistic reduced density matrix functional theory

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