344 research outputs found
A non-perturbative treatment of the generalized Su-Schreiffer-Heeger Hamiltonian on a dimer
Starting from the Hamiltonian for a dimer which includes all the electronic
and electron-phonon terms consistent with a non-degenerate orbital, by a
sequence of displacement and squeezing transformation we obtain an effective
polaronic Hamiltonian. The renormalized electronic interactions differ from the
results of semiclassical or perturbative treatments. The properties of the
variationally determined ground state of two particles in the orbital are
discussed for variable dimer length in the adiabatic limit.Comment: 6 pages, 3 figures, to be published in Int. Journal of Modern Physics
First principles study of electronic and structural properties of CuO
We investigate the electronic and structural properties of CuO, which shows
significant deviations from the trends obeyed by other transition-metal
monoxides. Using an extended Hubbard corrective functional, we uncover an
orbitally ordered insulating ground state for the cubic phase of this material,
which was expected but never found before. This insulating state results from a
fine balance between the tendency of Cu to complete its d-shell and Hund's rule
magnetism. Starting from the ground state for the cubic phase, we also study
tetragonal distortions of the unit cell (recently reported in experiments), the
consequent electronic reorganizations and identify the equilibrium structure.
Our calculations reveal an unexpected richness of possible magnetic and orbital
orders, relatively close in energy to the ground state, whose stability depends
on the sign and entity of distortion.Comment: 9 pages, 9 figure
Spin-state crossover and hyperfine interactions of ferric iron in MgSiO perovskite
Using density functional theory plus Hubbard calculations, we show that
the ground state of (Mg,Fe)(Si,Fe)O perovskite, a major mineral phase in
the Earth's lower mantle, has high-spin ferric iron () at both the
dodecahedral (A) and octahedral (B) site. As the pressure increases, the B-site
iron undergoes a spin-state crossover to the low-spin state (), while
the A-site iron remains in the high-spin state. Our calculation shows that the
B-site spin-state crossover in the pressure range of 40-70 GPa is accompanied
by a noticeable volume reduction and an increase in quadrupole splitting,
consistent with recent X-ray diffraction and M\"ossbauer spectroscopy
measurements. The volume reduction leads to a significant softening in the bulk
modulus, which suggests a possible source of seismic velocity anomalies in the
lower mantle.Comment: 11 pages, 4 figures, 1 tabl
Searching for high magnetization density in bulk Fe: the new metastable Fe phase
We report the discovery of a new allotrope of iron by first principles
calculations. This phase has symmetry, a six-atom unit cell (hence the
name Fe), and the highest magnetization density (M) among all known
crystalline phases of iron. Obtained from the structural optimizations of the
FeC-cementite crystal upon carbon removal, Fe is shown to
result from the stabilization of a ferromagnetic FCC phase, further strained
along the Bain path. Although metastable from 0 to 50 GPa, the new phase is
more stable, at low pressures, than the other well-known HCP and FCC allotropes
and smoothly transforms into the FCC phase under compression. If stabilized to
room temperature, e.g., by interstitial impurities, Fe could become the
basis material for high M rare-earth-free permanent magnets and high-impact
applications such as, light-weight electric engine rotors or high-density
recording media. The new phase could also be key to explain the enigmatic high
M of FeN, which is currently attracting an intense research
activity.Comment: 7 pages, 7 figure
Thermoelasticity of Fe2+-bearing bridgmanite
We present LDA+U calculations of high temperature elastic properties of
bridgmanite with composition (MgFe)SiO for
. Results of elastic moduli and acoustic velocities for the
Mg-end member (x=0) agree very well with the latest high pressure and high
temperature experimental measurements. In the iron-bearing system, we focus
particularly on the change in thermoelastic parameters across the state change
that occurs in ferrous iron above 30 GPa, often attributed to a high-spin
(HS) to intermediate spin (IS) crossover but explained by first principles
calculations as a lateral displacement of substitutional iron in the perovskite
cage. We show that the measured effect of this change on the equation of state
of this system can be explained by the lateral displacement of substitutional
iron, not by the HS to IS crossover. The calculated elastic properties of
(MgFe)SiO along an adiabatic mantle geotherm,
somewhat overestimate longitudinal velocities but produce densities and shear
velocities quite consistent with Preliminary Reference Earth Model data
throughout most of the lower mantle.Comment: Accepted for Geophysical Research Letters (DOI: 10.1002/2014GL062888
The different story of π bonds
We revisit “classical” issues in multiply bonded systems between main groups elements, namely the structural distortions that may occur at the multiple bonds and that lead, e.g., to trans-bent and bond-length alternated structures. The focus is on the role that orbital hybridization and electron correlation play in this context, here analyzed with the help of simple models for σ-and π-bonds, numerically exact solutions of Hubbard Hamiltonians and first principles (density functional theory) investigations of an extended set of systems
Fast approximations of activation functions in deep neural networks when using posit arithmetic
With increasing real-time constraints being put on the use of Deep Neural Networks (DNNs) by real-time scenarios, there is the need to review information representation. A very challenging path is to employ an encoding that allows a fast processing and hardware-friendly representation of information. Among the proposed alternatives to the IEEE 754 standard regarding floating point representation of real numbers, the recently introduced Posit format has been theoretically proven to be really promising in satisfying the mentioned requirements. However, with the absence of proper hardware support for this novel type, this evaluation can be conducted only through a software emulation. While waiting for the widespread availability of the Posit Processing Units (the equivalent of the Floating Point Unit (FPU)), we can already exploit the Posit representation and the currently available Arithmetic-Logic Unit (ALU) to speed up DNNs by manipulating the low-level bit string representations of Posits. As a first step, in this paper, we present new arithmetic properties of the Posit number system with a focus on the configuration with 0 exponent bits. In particular, we propose a new class of Posit operators called L1 operators, which consists of fast and approximated versions of existing arithmetic operations or functions (e.g., hyperbolic tangent (TANH) and extended linear unit (ELU)) only using integer arithmetic. These operators introduce very interesting properties and results: (i) faster evaluation than the exact counterpart with a negligible accuracy degradation; (ii) an efficient ALU emulation of a number of Posits operations; and (iii) the possibility to vectorize operations in Posits, using existing ALU vectorized operations (such as the scalable vector extension of ARM CPUs or advanced vector extensions on Intel CPUs). As a second step, we test the proposed activation function on Posit-based DNNs, showing how 16-bit down to 10-bit Posits represent an exact replacement for 32-bit floats while 8-bit Posits could be an interesting alternative to 32-bit floats since their performances are a bit lower but their high speed and low storage properties are very appealing (leading to a lower bandwidth demand and more cache-friendly code). Finally, we point out how small Posits (i.e., up to 14 bits long) are very interesting while PPUs become widespread, since Posit operations can be tabulated in a very efficient way (see details in the text)
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