Professor Yasutami Takada

Some of the recent research activities are as follows:
(1) Self-consistent calculation of the self-energy  (2) Dynamical structure factor (3) One-dimensional Hubbard-Holstein model (4) Four-body Coulomb system (5) A light atom in an electron gas (6) Jahn-Teller polaron (7) Stopping power of slow ions (8) Mechanism of superconductivity in the graphite intercalation compounds (9) Quantum transport in transition-metal oxides (10) Quantum phase transition of light

Some of the recent power-point files for one-hour presentation are as follows:
(1) On the improvement of the STLS theory (At Chiba Univ. in May 2008)
(2) On the theory beyond the GW approximation (at Benasque, Spain in September 2008)
(3) On the mechanism of superconductivity in the graphite intercalation compounds (at ISSP, in January 2009)

The history of my researches is summarized in the following:

I explain the research fields of our current interests.  

Interference of Correlated Electron Waves
  According to elementary textbooks on Solid State Physics, the band gap is formed by the Bragg reflection of electron waves. This statement is true if we can treat the electron-electron Coulomb interaction U in the Hartree-Fock approximation and the periodic potential due to ions V is small. However, if the effect of U is strong, the right starting point of the problem is to consider the eigenstates described by the Hamiltonian T+U, where T is the electron kinetic energy. A useful concept to represent the system of T+U is the quasi-particle picture in which each electron motion cannot be described by a single plain wave but rather a complicated combination of plain waves to form a wave packet. Thus the first thing we have to consider is the Bragg reflection of quasi-particles in the three-dimensional electron liquid.
  Such a consideration reveals that the renormalization factor z plays an important role in determining the band gap. In particular, if z vanishes as in a one-dimensional Tomonaga-Luttinger liquid, we find situations in which the band gap collapses even in the presence of V. This result can be understood easily in terms of the bosonization picture. In any way, we find that the concept of "the Luttinger liquid" is incompatible with that of "the Bragg reflection".
  We have also investigated the general crossover behavior from the case of T+V combined with weak U (the band picture) to that of T+U with weak V (the correlated-electron picture) by implementing the DMRG (Density-Matrix Renormalization-Group) calculation on a model in which V is added to the Hubbard model in one dimension. This study is of particular interest to those who consider a frustrated situation due to the competition of U and V in the crossover region from the band insulator to the Mott insulator. This illustrates the existence of a qualitatively distinct phase at the boundary between two phases which are not adiabatically connected. 
Related Materials: Charge-Transfer Organic Salts. Ferroelectric Materials.
Bloch Electrons in a Jahn-Teller Crystals
  It is well known that the Aharanov-Bohm effect operates in a molecule with the Jahn-Teller effect. However, no works have ever been done as to the investigation of the Berry-phase effect on the conduction-electron wavefunction in a system composed of a periodic array of Jahn-Teller centers.
  Recently, we have studied such a system and find, among others, (1) modification of the Bloch's theorem and (2) concept of the geometric energy in relation to the geometrically conserved winding number (Chern integers) which is introduced by parallel transport in the Berry-phase connection.From a standpoint of this concept, we have succeeded in explaing the competition between the bistripe and Wigner-crystal-like superstructures in the manganese. We are now extending our work to studying its effect on CMR. 
  We have done this work as an aspect to revise the Born-Oppenheimer adiabatic approximation. We are going to extend our study by including non-adiabatic processes (polarons). 
Related Materials: Perovskite Manganese Oxides (Specifically, their Stripe Structures)
Microscopic Mechanisms of Superconductivity
  In quantum mechanics, a state is determined by the negotiation of the kinetic energy (which makes particles itinerant) with the potential energy (which makes them localized). If the latter includes the interaction between particles, there appears a further complication due to the correlated motion of particles. We cannot avoid this intrinsic difficulty in quantum mechanics in elucidating the microscopic mechanism of superconductivity.
  An assembly of electrons, negatively charged particles with one-half spin, goes into the pair-condensed phase as a result of the competition between the mutual Coulomb repulsions and the phonon as well as spin-fluctuation mediated attractions. The physics of this charge-spin-phonon complex is the main themeof our research group.
  Specifically, we employ both the exact-diagonalization method and the Green's-function approach to study the electronic properties such as superconductivity, CDW, and SDW and their effects on the phonon properties in the Hubbard-Holstein model, because the model represents many features of the organic superconductors including the fullerenes.
  We have also embarked on improvements on the Eliashberg theory of superconductivity by the proper inclusion of the vertex corrections. As a first step for the purpose, we have found a general principle that an iterative operation of the Baym-Kadanoff's conserving approximation leads to the exact self-energy. Currently, we search an appropriate functional form for the self-energy revision operator, the core of the iterative method, by investigating the exact results in small-size systems.
Related Materials: Organic Superconductors. Copper-Oxide High-Temperature Suerconductors
Exchange and Correlation Effects in Solids
 Thanks to the rapid progress of computer technologies, we come to know accurate values for the static properties of quantum-mechanical many-body systems by using various sophisticated methods including the quantum Monte Carlo. Calculation of the dynamic properties, however, is still in its infancy. In terms of the Green's function method, this calculation is reduced to that of the vertex function. We have proposed a two-stage theory to obtain the vertex function: In the first stage, we have presented an algorithm introducing "the self-energy revision operator" which provides the exact self-energy as its invariant point. In the second stage, we invoke a physically-motivated approximation to the operator with taking full account of available resources of computation. 
 At present, the approximation is constructed using the Ward identity as well as the exchange-correlation factor, a key quantity to the time-dependent density-functional theory, in order to study the alkali metals. In the future, metals in general will be studied by this fundamental quantum theory of dynamics, a theory exceeding the GW approximation. 
 We are also interested in the exchange-correlation effect in the system with a very strong magnetic field applied to the electron liquid in two or three dimensions, in relation to the Laughlin state and graphite.
Related Materials: Simple and Transition Metals. Two-Dimensional Electron Systems at the Semiconductor-Insulator Interface and the Quasi-Two-Dimensional Electron System in Graphite in Strong Magnetic Fields.
Structural Phase Transition in Quantum Solids
 From diverse points of view, solid hydrogen and deuterium have been studied in a growing range of pressure and temperature in recent years. There has been agreement among several experimental research groups on the low-temperature phase diagrams for those solids at megabar pressures. On the theoretical side, structural and electronic properties of those phases have been extensively studied. 
 We study the effect of temperature up to 1000K, a rarely investigated range, on the structure of dense molecular para-hydrogen and ortho-deuterium, using the path-integral Monte Carlo method. We find that a structural phase transition occurs from orientationally disordered hexagonal close packed (hcp) to an orthorhombic structure of Cmca symmetry before melting. The transition is basically induced by thermal fluctuations, but quantum fluctuations of protons (deuterons) are also important in determining the transition temperature through "the quantum hardening effect". 
 We are now making a more detailed investigation of the effect of large quantum fluctuations of nuclei on the chemical bonding and possible connection with the quantum critical transition. 
Solid Hydrogen under Ultra-High Pressures. Electron-Hole and Exciton Systems in Degenerate Semiconductors.