788 research outputs found
Effective Hamiltonian for transition-metal compounds. Application to Na_xCoO_2
We describe a simple scheme to construct a low-energy effective Hamiltonian
H_eff for highly correlated systems containing non-metals like O, P or As (O in
what follows) and a transition-metal (M) as the active part in the electronic
structure, eliminating the O degrees of freedom from a starting Hamiltonian
that contains all M d orbitals and all non-metal p orbitals. We calculate all
interaction terms between d electrons originating from Coulomb repulsion, as a
function of three parameters (F_0, F_2 and F_4) and write them in a basis of
orbitals appropriate for cubic, tetragonal, tetrahedral or hexagonal symmetry
around M. The approach is based on solving exactly (numerically if necessary) a
MO_n cluster containing the transition-metal atom and its n nearest O atoms
(for example a CoO_6 cluster in the case of the cobaltates, or a CuO_n cluster
in the case of the cuprates, in which n depends on the number of apical O
atoms), and mapping them into many-body states of the same symmetry containing
d holes only. We illustrate the procedure for the case of Na_xCoO_2. The
resulting H_eff, including a trigonal distortion D, has been studied recently
and its electronic structure agrees well with angle-resolved photoemission
spectra [A. Bourgeois, A. A. Aligia, and M. J. Rozenberg, Phys. Rev. Lett. 102,
066402 (2009)]. Although H_eff contains only 3d t_2g holes, the highly
correlated states that they represent contain an important amount not only of O
2p holes but also of 3d e_g holes. When more holes are added, a significant
redistribution of charge takes place. As a consequence of these facts, the
resulting values of the effective interactions between t_2g states are smaller
than previously assumed, rendering more important the effect of D in obtaining
only one sheet around the center of the Brillouin zone for the Fermi surface
(without additional pockets).Comment: 11 pages, 1 figure, accepted for publication in Phys.Rev.
Symmetries and collective excitations in large superconducting circuits
The intriguing appeal of circuits lies in their modularity and ease of
fabrication. Based on a toolbox of simple building blocks, circuits present a
powerful framework for achieving new functionality by combining circuit
elements into larger networks. It is an open question to what degree modularity
also holds for quantum circuits -- circuits made of superconducting material,
in which electric voltages and currents are governed by the laws of quantum
physics. If realizable, quantum coherence in larger circuit networks has great
potential for advances in quantum information processing including topological
protection from decoherence. Here, we present theory suitable for quantitative
modeling of such large circuits and discuss its application to the fluxonium
device. Our approach makes use of approximate symmetries exhibited by the
circuit, and enables us to obtain new predictions for the energy spectrum of
the fluxonium device which can be tested with current experimental technology
The higher order C_n dispersion coefficients for the alkali atoms
The van der Waals coefficients, from C_11 through to C_16 resulting from 2nd,
3rd and 4th order perturbation theory are estimated for the alkali (Li, Na, K
and Rb) atoms. The dispersion coefficients are also computed for all possible
combinations of the alkali atoms and hydrogen. The parameters are determined
from sum-rules after diagonalizing the fixed core Hamiltonian in a large basis.
Comparisons of the radial dependence of the C_n/r^n potentials give guidance as
to the radial regions in which the various higher-order terms can be neglected.
It is seen that including terms up to C_10/r^10 results in a dispersion
interaction that is accurate to better than 1 percent whenever the
inter-nuclear spacing is larger than 20 a_0. This level of accuracy is mainly
achieved due to the fortuitous cancellation between the repulsive (C_11, C_13,
C_15) and attractive (C_12, C_14, C_16) dispersion forces.Comment: 8 pages, 7 figure
Coulomb correlation in presence of spin-orbit coupling: application to plutonium
Attempts to go beyond the local density approximation (LDA) of Density
Functional Theory (DFT) have been increasingly based on the incorporation of
more realistic Coulomb interactions. In their earliest implementations, methods
like LDA+, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used
a simple model interaction . In this article we generalize the solution of
the full Coulomb matrix involving to parameters, which is
usually presented in terms of an basis, into a basis of
the total angular momentum, where we also include spin-orbit coupling; this
type of theory is needed for a reliable description of -state elements like
plutonium, which we use as an example of our theory. Close attention will be
paid to spin-flip terms, which are important in multiplet theory but that have
been usually neglected in these kinds of studies. We find that, in a
density-density approximation, the basis results provide a very good
approximation to the full Coulomb matrix result, in contrast to the much less
accurate results for the more conventional basis
Alternative Mathematical Technique to Determine LS Spectral Terms
We presented an alternative computational method for determining the
permitted LS spectral terms arising from electronic configurations. This
method makes the direct calculation of LS terms possible. Using only basic
algebra, we derived our theory from LS-coupling scheme and Pauli exclusion
principle. As an application, we have performed the most complete set of
calculations to date of the spectral terms arising from electronic
configurations, and the representative results were shown. As another
application on deducing LS-coupling rules, for two equivalent electrons, we
deduced the famous Even Rule; for three equivalent electrons, we derived a new
simple rule.Comment: Submitted to Phys. Rev.
Systematic computation of crystal field multiplets for X-ray core spectroscopies
We present a new approach to computing multiplets for core spectroscopies,
whereby the crystal field is constructed explicitly from the positions and
charges of surrounding atoms. The simplicity of the input allows the
consideration of crystal fields of any symmetry, and in particular facilitates
the study of spectroscopic effects arising from low symmetry environments. The
interplay between polarization directions and crystal field can also be
conveniently investigated. The determination of the multiplets proceeds from a
Dirac density functional atomic calculation, followed by the exact
diagonalization of the Coulomb, spin-orbit and crystal field interactions for
the electrons in the open shells. The eigenstates are then used to simulate
X-ray Absorption Spectroscopy and Resonant Inelastic X-ray Scattering spectra.
In examples ranging from high symmetry down to low symmetry environment,
comparisons with experiments are done with unadjusted model parameters as well
as with semi-empirically optimized ones. Furthermore, predictions for the RIXS
of low-temperature MnO and for Dy in a molecular complex are proposed.Comment: Accepted for publication in Phys. Rev.
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