29 research outputs found
Projected site-occupation embedding theory
Site-occupation embedding theory (SOET) [B. Senjean et al., Phys. Rev. B 97,
235105 (2018)] is an in-principle exact embedding method combining wavefunction
theory and density functional theory that gave promising results when applied
to the one-dimensional Hubbard model. Despite its overall good performance,
SOET faces a computational cost problem as its auxiliary impurity-interacting
system remains the size of the full system (which is problematic as the
computational cost increases exponentially with system size). In this work,
this issue is circumvented by employing the Schmidt decomposition, thus leading
to a drastic reduction of the computational cost while retaining the same
accuracy. We show that this projected version of SOET (P-SOET) is competitive
with other embedding techniques such as density matrix embedding theory (DMET)
[G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. In contrast
to the latter, density functional contributions come naturally into play in
P-SOET's framework without any additional computational cost or double counting
effect. As an important result, the density-driven Mott-Hubbard transition
(which is displayed by multiple impurity sites in DMET or in dynamical
mean-field theory) is well described, for the first time, with a single
impurity site.Comment: 11 pages, 11 figures, 1 Tabl
N-centered ensemble density-functional theory for open systems
Two (so-called left and right) variants of N-centered ensemble
density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513
(2018)] are presented. Unlike the original formulation of the theory, these
variants allow for the description of systems with a fractional electron
number. While conventional DFT for open systems uses only the true electron
density as basic variable, left/right N-centered ensemble DFT relies instead on
(i) a fictitious ensemble density that integrates to a central (integral)
number N of electrons, and (ii) a grand canonical ensemble weight
which is equal to the deviation of the true electron number from N. Within such
a formalism, the infamous derivative discontinuity that appears when crossing
an integral number of electrons is described exactly through the dependence in
of the left and right N-centered ensemble Hartree-exchange-correlation
density functionals. Incorporating N-centered ensembles into existing
density-functional embedding theories is expected to pave the way towards the
in-principle-exact description of an open fragment by means of a pure-state
N-electron many-body wavefunction. Work is currently in progress in this
directionComment: 15 pages, 4 figures, 1 tabl
Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
Site-occupation embedding theory (SOET) is an alternative formulation of
density-functional theory (DFT) for model Hamiltonians where the
fully-interacting Hubbard problem is mapped, in principle exactly, onto an
impurity-interacting (rather than a non-interacting) one. It provides a
rigorous framework for combining wavefunction (or Green function) based methods
with DFT. In this work, exact expressions for the per-site energy and double
occupation of the uniform Hubbard model are derived in the context of SOET. As
readily seen from these derivations, the so-called bath contribution to the
per-site correlation energy is, in addition to the latter, the key density
functional quantity to model in SOET. Various approximations based on Bethe
ansatz and perturbative solutions to the Hubbard and single impurity Anderson
models are constructed and tested on a one-dimensional ring. The
self-consistent calculation of the embedded impurity wavefunction has been
performed with the density matrix renormalization group method. It has been
shown that promising results are obtained in specific regimes of correlation
and density. Possible further developments have been proposed in order to
provide reliable embedding functionals and potentials.Comment: Regular article with 14 pages including 6 figure
Recursive relations and quantum eigensolver algorithms within modified Schrieffer--Wolff transformations for the Hubbard dimer
We derive recursive relations for the Schrieffer--Wolff (SW) transformation
applied to the half-filled Hubbard dimer. While the standard SW transformation
is set to block-diagonalize the transformed Hamiltonian solely at the first
order of perturbation, we infer from recursive relations two types of
modifications, variational or iterative, that approach, or even enforce for the
homogeneous case, the desired block-diagonalization at infinite order of
perturbation. The modified SW unitary transformations are then used to design
an test quantum algorithms adapted to the noisy and fault-tolerant era. This
work paves the way toward the design of alternative quantum algorithms for the
general Hubbard Hamiltonian
Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states
Gross-Oliveira-Kohn density functional theory (GOK-DFT) for ensembles is in
principle very attractive, but has been hard to use in practice. A novel,
practical model based on GOK-DFT for the calculation of electronic excitation
energies is discussed. The new model relies on two modifications of GOK-DFT:
use of range separation and use of the slope of the linearly-interpolated
ensemble energy, rather than orbital energies. The range-separated approach is
appealing as it enables the rigorous formulation of a multi-determinant
state-averaged DFT method. In the exact theory, the short-range density
functional, that complements the long-range wavefunction-based ensemble energy
contribution, should vary with the ensemble weights even when the density is
held fixed. This weight dependence ensures that the range-separated ensemble
energy varies linearly with the ensemble weights. When the (weight-independent)
ground-state short-range exchange-correlation functional is used in this
context, curvature appears thus leading to an approximate weight-dependent
excitation energy. In order to obtain unambiguous approximate excitation
energies, we propose to interpolate linearly the ensemble energy between
equiensembles. It is shown that such a linear interpolation method (LIM) can be
rationalized and that it effectively introduces weight dependence effects. As
proof of principle, LIM has been applied to He, Be, H in both equilibrium
and stretched geometries as well as the stretched HeH molecule. Very
promising results have been obtained for both single (including charge
transfer) and double excitations with spin-independent short-range local and
semi-local functionals. Even at the Kohn--Sham ensemble DFT level, that is
recovered when the range-separation parameter is set to zero, LIM performs
better than standard time-dependent DFT.Comment: 26 pages, 8 figure
A quantum advantage for Density Functional Theory ?
The technological revolution brought about by quantum computers promises to
solve problems with high economical and societal impact that remain intractable
on classical computers. While several quantum algorithms have been devoted to
solve the many-body problem in quantum chemistry, the focus is on wavefunction
theory that is limited to relatively small systems, even for quantum computers,
i.e., the size of tractable systems being roughly limited by the number of
qubits available. Computations on large systems rely mainly on mean-field-type
approaches such as density functional theory, for which no quantum advantage
has been envisioned so far. In this work, we question this a priori by
investigating the benefit of quantum computers to scale up not only many-body
wavefunction methods, but also mean-field-type methods, and consequently the
all range of application of quantum chemistry.Comment: 9 pages, 3 figure
Characterization of Excited States in Time-Dependent Density Functional Theory Using Localized Molecular Orbitals
Localized molecular orbitals are often used for the analysis of chemical
bonds, but they can also serve to efficiently and comprehensibly compute linear
response properties. While conventional canonical molecular orbitals provide an
adequate basis for the treatment of excited states, a chemically meaningful
identification of the different excited-state processes is difficult within
such a delocalized orbital basis. In this work, starting from an initial set of
supermolecular canonical molecular orbitals, we provide a simple one-step
top-down embedding procedure for generating a set of orbitals which are
localized in terms of the supermolecule, but delocalized over each subsystem
composing the supermolecule. Using an orbital partitioning scheme based on such
sets of localized orbitals, we further present a procedure for the construction
of local excitations and charge-transfer states within the linear response
framework of time-dependent density functional theory (TDDFT). This procedure
provides direct access to approximate diabatic excitation energies and, under
the Tamm--Dancoff approximation, also their corresponding electronic couplings
-- quantities that are of primary importance in modelling energy transfer
processes in complex biological systems. Our approach is compared with a
recently developed diabatization procedure based on subsystem TDDFT using
projection operators, which leads to a similar set of working equations.
Although both of these methods differ in the general localization strategies
adopted and the type of basis functions (Slaters vs. Gaussians) employed, an
overall decent agreement is obtained