113 research outputs found
Dealing with the exponential wall in electronic structure calculations
An alternative to Density Functional Theory are wavefunction based electronic
structure calculations for solids. In order to perform them the Exponential
Wall (EW) problem has to be resolved. It is caused by an exponential increase
of the number of configurations with increasing electron number N. There are
different routes one may follow. One is to characterize a many-electron
wavefunction by a vector in Liouville space with a cumulant metric rather than
in Hilbert space. This removes the EW problem. Another is to model the solid by
an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated
at a much lower level than the former. This is the case in Density Matrix
Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are
closely related to a Schmidt decomposition of a system and to the determination
of the associated entanglement. We show here the connection between the two
approaches. It turns out that the DMET (or DET) has an identical active space
as a previously used Local Ansatz, based on a projection and partitioning
approach. Yet, the EW problem is resolved differently in the two cases. By
studying a ring these differences are analyzed with the help of the
method of increments.Comment: 19 pages, 5 figure
Ground-state wavefunction of macroscopic electron systems
Wavefunctions for large electron numbers are plagued by the Exponential
Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert
space with . Therefore they loose their meaning for macroscopic systems, a
point stressed in particular by W. Kohn. The EWP has to be resolved in order to
be able to perform electronic structure calculations, e.g., for solids. The
origin of the EWP is the multiplicative property of wavefunctions when
independent subsystems are considered. Therefore it can only be avoided when
wavefunctions are formulated so that they are additive instead, in particular
when matrix elements involving them are calculated. We describe how this is
done for the ground state of a macroscopic electron system. Going over from a
multiplicative to an additive quantity requires taking a logarithm. Here it
implies going over from Hilbert space to the operator- or Liouville space with
a metric based on cumulants. The operators which define the ground-state
wavefunction generate fluctuations from a mean-field state. The latter does not
suffer from an EWP and therefore may serve as a vacuum state. The fluctuations
have to be {\it connected} like the ones caused by pair interactions in a
classical gas when the free energy is calculated (Meyer's cluster expansion).
This fixes the metric in Liouville space. The scheme presented here provides a
solid basis for electronic structure calculations for the ground state of
solids. In fact, its applicability has already been proven. We discuss also
matrix product states, which have been applied to one-dimensional systems with
results of high precision. Although these states are formulated in Hilbert
space they are processed by using operators in Liouville space. We show that
they fit into the general formalism described above.Comment: 29 pages, 3 figure
Field dependent mass enhancement in Pr_{1-x}La_xOs_4Sb_12 from aspherical Coulomb scattering
The scattering of conduction electrons by crystalline electric field (CEF)
excitations may enhance their effective quasiparticle mass similar to
scattering from phonons. A wellknown example is Pr metal where the isotropic
exchange scattering from inelastic singlet-singlet excitations causes the mass
enhancement. An analogous mechanism may be at work in the skutterudite
compounds Pr_{1-x}La_xOs_4Sb_12 where close to x=1 the compound develops heavy
quasiparticles with a large linear specific heat coefficient. There the low
lying CEF states are singlet ground state and a triplet at 8 K. Due to the
tetrahedral CEF the main scattering mechanism must be the aspherical Coulomb
scattering. We derive the expression for mass enhancement in this model
including also the case of dispersive excitations. We show that for small to
moderate dispersion there is a strongly field dependent mass enhancement due to
the field induced triplet splitting. It is suggested that this effect may be
seen in Pr_{1-x}La_xOs_4Sb_12 with suitably large x when the dispersion is
small.Comment: 12 pages, 5 figure
Ab-Initio Calculation of the Metal-Insulator Transition in Lithium rings
We study how the Mott metal-insulator transition (MIT) is affected when we
have to deal with electrons with different angular momentum quantum numbers.
For that purpose we apply ab-initio quantum-chemical methods to lithium rings
in order to investigate the analogue of a MIT. By changing the interatomic
distance we analyse the character of the many-body wavefunction and discuss the
importance of the orbital quasi-degeneracy within the metallic regime.
The charge gap (ionization potential minus electron affinity) shows a minimum
and the static electric dipole polarizability has a pronounced maximum at a
lattice constant where the character of the wavefunction changes from
significant to essentially -type. In addition, we examine rings with
bond alternation in order to answer the question under which conditions a
Peierls distortion occurs.Comment: 9 pages, 11 figure
Obtaining Wannier Functions of a Crystalline Insulator within a Hartree-Fock approach: Applications to LiF and LiCl
An ab initio Hartree-Fock approach aimed at directly obtaining the localized
orthogonal orbitals (Wannier functions) of a crystalline insulator is described
in detail. The method is used to perform all-electron calculations on the
ground states of crystalline lithium fluoride and lithium chloride, without the
use of any pseudo or model potentials. Quantities such as total energy, x-ray
structure factors and Compton profiles obtained using the localized
Hartree-Fock orbitals are shown to be in excellent agreement with the
corresponding quantities calculated using the conventional Bloch-orbital based
Hartree-Fock approach. Localization characteristics of these orbitals are also
discussed in detail.Comment: 39 Pages, RevTex, 4 postscript figures, to appear in PRB15, January
9
Wavefunction-based correlated ab initio calculations on crystalline solids
We present a wavefunction-based approach to correlated ab initio calculations
on crystalline insulators of infinite extent. It uses the representation of the
occupied and the unoccupied (virtual) single-particle states of the infinite
solid in terms of Wannier functions. Electron correlation effects are evaluated
by considering virtual excitations from a small region in and around the
reference cell, keeping the electrons of the rest of the infinite crystal
frozen at the Hartree-Fock level. The method is applied to study the ground
state properties of the LiH crystal, and is shown to yield rapidly convergent
results.Comment: 6 pages, RevTex, to appear in Phys. Rev.
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