69 research outputs found
A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
We introduce a mean-field and perturbative approach, based on clusters, to
describe the ground state of fermionic strongly-correlated systems. In cluster
mean-field, the ground state wavefunction is written as a simple tensor product
over optimized cluster states. The optimization of the single-particle basis
where the cluster mean-field is expressed is crucial in order to obtain
high-quality results. The mean-field nature of the ansatz allows us to
formulate a perturbative approach to account for inter-cluster correlations;
other traditional many-body strategies can be easily devised in terms of the
cluster states. We present benchmark calculations on the half-filled 1D and
(square) 2D Hubbard model, as well as the lightly-doped regime in 2D, using
cluster mean-field and second-order perturbation theory. Our results indicate
that, with sufficiently large clusters or to second-order in perturbation
theory, a cluster-based approach can provide an accurate description of the
Hubbard model in the considered regimes. Several avenues to improve upon the
results presented in this work are discussed.Comment: 22 pages, 21 figure
Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
Most {\em ab initio} calculations on fullerene molecules have been carried
out based on the paradigm of the H\"uckel model. This is consistent with the
restricted nature of the independent-particle model underlying such
calculations, even in single-reference-based correlated approaches. On the
other hand, previous works on some of these molecules using model Hamiltonians
have clearly indicated the importance of short-range inter-atomic spin-spin
correlations. In this work, we consider {\em ab initio} non-collinear
Hartree--Fock (HF) solutions for representative fullerene systems: the bowl,
cage, ring, and pentagon isomers of C, and the larger C,
C, C, C, and C fullerene cages. In all cases but
the ring we find that the HF minimum corresponds to a truly non-collinear
solution with a torsional spin density wave. Optimized geometries at the
generalized HF (GHF) level lead to fully symmetric structures, even in those
cases where Jahn-Teller distortions have been previously considered. The nature
of the GHF solutions is consistent with the -electron space becoming
polyradical in nature: each -orbital remains effectively singly occupied.
The spin frustration, induced by the pentagon rings in an otherwise
anti-ferromagnetic background, is minimized at the HF level by aligning the
spins in non-collinear arrangements. The long-range magnetic ordering observed
is reminiscent of the character of broken symmetry HF solutions in polyacene
systems.Comment: 16 figure
Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
A multi-reference configuration mixing scheme is used to describe the ground
state, characterized by well defined spin and space group symmetry quantum
numbers as well as doping fractions , of one dimensional
Hubbard lattices with nearest-neighbor hopping and periodic boundary
conditions. Within this scheme, each ground state is expanded in a given number
of nonorthogonal and variationally determined symmetry-projected
configurations. The results obtained for the ground state and correlation
energies of half-filled and doped lattices with 30, 34 and 50 sites, compare
well with the exact Lieb-Wu solutions as well as with the ones obtained with
other state-of-the-art approximations. The structure of the intrinsic
symmetry-broken determinants resulting from the variational procedure is
interpreted in terms of solitons whose translational and breathing motions can
be regarded as basic units of quantum fluctuations. It is also shown that in
the case of doped 1D lattices, a part of such fluctuations can also be
interpreted in terms of polarons. In addition to momentum distributions, both
spin-spin and density-density correlation functions are studied as functions of
doping. The spectral functions and density of states, computed with an ansatz
whose quality can be well-controlled by the number of symmetry-projected
configurations used to approximate the electron systems, display
features beyond a simple quasiparticle distribution, as well as spin-charge
separation trends.Comment: 16 pages, 11 figure
Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
Recent work on approximating ground states of Heisenberg spin clusters by
projected Hartree-Fock theory (PHF) is extended to a cluster-based ansatz
(cPHF). Whereas PHF variationally optimizes a site-spin product state for the
restoration of spin- and point-group symmetry, cPHF groups sites into discrete
clusters and uses a cluster-product state as the broken-symmetry reference.
Intracluster correlation is thus already included at the mean-field level and
intercluster correlation is introduced through symmetry projection. Variants of
cPHF differing in the broken and restored symmetries are evaluated for ground
states and singlet-triplet gaps of antiferromagnetic spin rings for various
cluster sizes, where cPHF in general affords a significant improvement over
ordinary PHF, although the division into clusters lowers the cyclical symmetry.
On the other hand, certain two- or three-dimensional spin arrangements permit
cluster groupings compatible with the full spatial symmetry. We accordingly
demonstrate that cPHF yields approximate ground states with correct spin and
point-group quantum numbers for honeycomb lattice fragments and symmetric
polyhedra.Comment: 41 page
Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories
This paper explores the possibility of combining projected Hartree-Fock and density functional theories
for treating static and dynamic correlations in molecular systems with mean-field computational
cost. The combination of spin-projected unrestricted Hartree-Fock (SUHF) with the TPSS correlation
functional (SUHF+TPSS) yields excellent results for non-metallic molecular dissociations and
singlet-triplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation
curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters
and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve
shape for Cr2 can be obtained; unfortunately, such a combination is found to lead to overcorrelation
in the general case
Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations
Recent work from our research group has demonstrated that symmetry-projected
Hartree--Fock (HF) methods provide a compact representation of molecular ground
state wavefunctions based on a superposition of non-orthogonal Slater
determinants. The symmetry-projected ansatz can account for static correlations
in a computationally efficient way. Here we present a variational extension of
this methodology applicable to excited states of the same symmetry as the
ground state. Benchmark calculations on the C dimer with a modest basis
set, which allows comparison with full configuration interaction results,
indicate that this extension provides a high quality description of the
low-lying spectrum for the entire dissociation profile. We apply the same
methodology to obtain the full low-lying vertical excitation spectrum of
formaldehyde, in good agreement with available theoretical and experimental
data, as well as to a challenging model insertion pathway for BeH.
The variational excited state methodology developed in this work has two
remarkable traits: it is fully black-box and will be applicable to fairly large
systems thanks to its mean-field computational cost
Calculation of molecular g-tensors by sampling spin orientations of generalised Hartree-Fock states
The variational inclusion of spin-orbit coupling in self-consistent field
(SCF) calculations requires a generalised two-component framework, which
permits the single-determinant wave function to completely break spin symmetry.
The individual components of the molecular g-tensor are commonly obtained from
separate SCF solutions that align the magnetic moment along one of the three
principal tensor axes. However, this strategy raises the question if energy
differences between solutions are relevant, or how convergence is achieved if
the principal axis system is not determined by molecular symmetry. The present
work resolves these issues by a simple two-step procedure akin to the generator
coordinate method (GCM). First, a few generalised Hartree Fock (GHF) solutions
are converged, applying, where needed, a constraint to the orientation of the
magnetic-moment or spin vector. Then, superpositions of GHF determinants are
formed through non-orthogonal configuration interaction. This procedure yields
a Kramers doublet for the calculation of the complete g-tensor. Alternatively,
for systems with weak spin-orbit effects, diagonalisation in a basis spanned by
spin rotations of a single GHF determinant affords qualitatively correct
g-tensors by eliminating errors related to spin contamination. For small
first-row molecules, these approaches are evaluated against experimental data
and full configuration interaction results. It is further demonstrated for two
systems (a fictitious tetrahedral CH4+ species, and a CuF4(2-) complex) that a
GCM strategy, in contrast to alternative mean-field methods, can correctly
describe the spin-orbit splitting of orbitally-degenerate ground states, which
causes large g-shifts and may lead to negative g-values.Comment: 33 pages, 5 figur
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