12,895 research outputs found
Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
The past several years have seen renewed interest in the use of
symmetry-projected Hartree-Fock for the description of strong correlations.
Unfortunately, these symmetry-projected mean-field methods do not adequately
account for dynamic correlation. Presumably, this shortcoming could be
addressed if one could combine symmetry-projected Hartree-Fock with a many-body
method such as coupled cluster theory, but this is by no means straightforward
because the two techniques are formulated in very different ways. However, we
have recently shown that the singlet -projected unrestricted Hartree-Fock
wave function can in fact be written in a coupled cluster-like wave function:
that is, the spin-projected unrestricted Hartree-Fock wave function can be
written as a polynomial of a double-excitation operator acting on some
closed-shell reference determinant. Here, we extend this result and show that
the spin-projected generalized Hartree-Fock wave function (which has both
and projection) is likewise a polynomial of low-order excitation
operators acting on a closed-shell determinant, and provide a closed-form
expression for the resulting polynomial coefficients. We include a few
preliminary applications of the combination of this spin-projected Hartree-Fock
and coupled cluster theory to the Hubbard Hamiltonian, and comment on
generalizations of the methodology. Results here are not for production level,
but a similarity transformed theory that combines the two offers the promise of
being accurate for both weak and strong correlation, and particularly may offer
significant improvements in the intermediate correlation regime where neither
projected Hartree-Fock nor coupled cluster is particularly accurate.Comment: accepted by Phys. Rev.
Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
Spin-projected Hartree-Fock is introduced as a particle-hole excitation
ansatz over a symmetry-adapted reference determinant. Remarkably, this
expansion has an analytic expression that we were able to decipher. While the
form of the polynomial expansion is universal, the excitation amplitudes need
to be optimized. This is equivalent to the optimization of orbitals in the
conventional projected Hartree-Fock framework of non-orthogonal determinants.
Using the inverse of the particle-hole expansion, we similarity transform the
Hamiltonian in a coupled-cluster style theory. The left eigenvector of the
non-hermitian Hamiltonian is constructed in a similar particle-hole expansion
fashion, and we show that to numerically reproduce variational projected
Hartree-Fock results, one needs as many pair excitations in the bra as the
number of strongly correlated entangled pairs in the system. This
single-excitation polynomial similarity transformation theory is an alternative
to our recently presented double excitation theory, but supports projected
Hartree-Fock and coupled cluster simultaneously rather than interpolating
between them
Quasiparticle Coupled Cluster Theory for Pairing Interactions
We present an extension of the pair coupled cluster doubles (p-CCD) method to
quasiparticles and apply it to the attractive pairing Hamiltonian. Near the
transition point where number symmetry gets spontaneously broken, the proposed
BCS-based p-CCD method yields significantly better energies than existing
methods when compared to exact results obtained via solution of the Richardson
equations. The quasiparticle p-CCD method has a low computational cost of
as a function of system size. This together with the high
quality of results here demonstrated, points to considerable promise for the
accurate description of strongly correlated systems with more realistic pairing
interactions
Hartree-Fock symmetry breaking around conical intersections
We study the behavior of Hartree-Fock (HF) solutions in the vicinity of
conical intersections. These are here understood as regions of a molecular
potential energy surface characterized by degenerate or nearly-degenerate
eigenfunctions with identical quantum numbers (point group, spin, and electron
number). Accidental degeneracies between states with different quantum numbers
are known to induce symmetry breaking in HF. The most common closed-shell
restricted HF instability is related to singlet-triplet spin degeneracies that
lead to collinear unrestricted HF (UHF) solutions. Adding geometric frustration
to the mix usually results in noncollinear generalized HF (GHF) solutions,
identified by orbitals that are linear combinations of up and down spins. Near
conical intersections, we observe the appearance of coplanar GHF solutions that
break all symmetries, including complex conjugation and time-reversal, which do
not carry good quantum numbers. We discuss several prototypical examples taken
from the conical intersection literature. Additionally, we utilize a recently
introduced a magnetization diagnostic to characterize these solutions, as well
as a solution of a Jahn-Teller active geometry of H.Comment: accepted to JCP December 2017, published online January 201
Range Separated Brueckner Coupled Cluster Doubles Theory
We introduce a range-separation approximation to coupled cluster doubles
(CCD) theory that successfully overcomes limitations of regular CCD when
applied to the uniform electron gas. We combine the short-range ladder channel
with the long-range ring channel in the presence of a Bruckner renormalized
one-body interaction and obtain ground-state energies with an accuracy of 0.001
a.u./electron across a wide range of density regimes. Our scheme is
particularly useful in the low-density and strongly-correlated regimes, where
regular CCD has serious drawbacks. Moreover, we cure the infamous
overcorrelation of approaches based on ring diagrams (i.e. the particle-hole
random phase approximation). Our energies are further shown to have appropriate
basis set and thermodynamic limit convergence, and overall this scheme promises
energetic properties for realistic periodic and extended systems which existing
methods do not possess.Comment: 5 pages, 3 figs. Now with supplementary info. Comments welcome:
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