5,230 research outputs found
Determination of the Mott insulating transition by the multi-reference density functional theory
It is shown that a momentum-boost technique applied to the extended Kohn-Sham
scheme enables the computational determination of the Mott insulating
transition. Self-consistent solutions are given for correlated electron systems
by the first-principles calculation defined by the multi-reference density
functional theory, in which the effective short-range interaction can be
determined by the fluctuation reference method. An extension of the Harriman
construction is made for the twisted boundary condition in order to define the
momentum-boost technique in the first-principles manner. For an effectively
half-filled-band system, the momentum-boost method tells that the period of a
metallic ground state by the LDA calculation is shortened to the least period
of the insulating phase, indicating occurrence of the Mott insulating
transition.Comment: 5 pages, 1 figure, to appear in J. Phys. Condens. Matte
Oka properties of complements of holomorphically convex sets
Our main theorem states that the complement of a compact holomorphically
convex set in a Stein manifold with the density property is an Oka manifold.
This gives a positive answer to the well-known long-standing problem in Oka
theory whether the complement of a polynomially convex set in
is Oka. Furthermore, we obtain new examples of nonelliptic Oka
manifolds which negatively answer Gromov's question. The relative version of
the main theorem is also proved. As an application, we show that the complement
of a totally real affine subspace is
Oka if and .Comment: 15 page
Elliptic characterization and localization of Oka manifolds
We prove that Gromov's ellipticity condition characterizes
Oka manifolds. This characterization gives another proof of the fact that
subellipticity implies the Oka property, and affirmative answers to Gromov's
conjectures. As another application, we establish the localization principle
for Oka manifolds, which gives new examples of Oka manifolds. In the appendix,
it is also shown that the Oka property is not a bimeromorphic invariant.Comment: 15 page
Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps
We study when there exists a dense holomorphic curve in a space of
holomorphic maps from a Stein space. We first show that for any bounded convex
domain and any connected complex manifold , the
space contains a dense holomorphic disc. Our second
result states that is an Oka manifold if and only if for any Stein space
there exists a dense entire curve in every path component of
.
In the second half of this paper, we apply the above results to the theory of
universal functions. It is proved that for any bounded convex domain
, any fixed-point-free automorphism of and
any connected complex manifold , there exists a universal map .
We also characterize Oka manifolds by the existence of universal maps.Comment: 15 page
A self-consistent first-principles calculation scheme for correlated electron systems
A self-consistent calculation scheme for correlated electron systems is
created based on the density-functional theory (DFT). Our scheme is a
multi-reference DFT (MR-DFT) calculation in which the electron charge density
is reproduced by an auxiliary interacting Fermion system. A short-range
Hubbard-type interaction is introduced by a rigorous manner with a residual
term for the exchange-correlation energy. The Hubbard term is determined
uniquely by referencing the density fluctuation at a selected localized
orbital. This strategy to obtain an extension of the Kohn-Sham scheme provides
a self-consistent electronic structure calculation for the materials design.
Introducing an approximation for the residual exchange-correlation energy
functional, we have the LDA+U energy functional. Practical self-consistent
calculations are exemplified by simulations of Hydrogen systems, i.e. a
molecule and a periodic one-dimensional array, which is a proof of existence of
the interaction strength U as a continuous function of the local fluctuation
and structural parameters of the system.Comment: 23 pages, 8 figures, to appear in J. Phys. Condens. Matte
Determination of Boundary Scattering, Intermagnon Scattering, and the Haldane Gap in Heisenberg Chains
Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain
is analyzed using the non-Abelian DMRG method. The scattering length of the boundary coupling and the inter-magnon scattering length are
determined. The scattering length is found to exhibit a
characteristic diverging behavior at the crossover point. In contrast, the
Haldane gap , the magnon velocity , and remain constant at the
crossover. Our method allowed estimation of the gap of the S=2 AF chain to be
using a chain length longer than the correlation length
.Comment: 6 pages, 3 figures, 1 table, accepted in Phys. Rev.
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