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 $\mathbb{C}^{n}$ $(n>1)$ 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 $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ of a totally real affine subspace is Oka if $n>1$ and $(n,k)\neq(2,1),(2,2),(3,3)$.Comment: 15 page

Elliptic characterization and localization of Oka manifolds

We prove that Gromov's ellipticity condition $\mathrm{Ell}_1$ 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 $\Omega\Subset\mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc. Our second result states that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. 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 $\Omega\Subset\mathbb{C}^n$, any fixed-point-free automorphism of $\Omega$ and any connected complex manifold $Y$, there exists a universal map $\Omega\to Y$. 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 $a_{\rm b}$ of the boundary coupling and the inter-magnon scattering length $a$ are determined. The scattering length $a_{\rm b}$ is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap $\Delta$, the magnon velocity $v$, and $a$ remain constant at the crossover. Our method allowed estimation of the gap of the S=2 AF chain to be $\Delta = 0.0891623(9)$ using a chain length longer than the correlation length $\xi$.Comment: 6 pages, 3 figures, 1 table, accepted in Phys. Rev.