I explain the research fields of our current interests.

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
electronelectron Coulomb interaction U in the HartreeFock 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
quasiparticle 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 quasiparticles in the threedimensional 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 onedimensional TomonagaLuttinger 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 correlatedelectron picture) by implementing the DMRG (DensityMatrix RenormalizationGroup) 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: ChargeTransfer Organic Salts. Ferroelectric Materials. 

It is well known that the AharanovBohm effect operates in
a molecule with the JahnTeller effect. However,
no works have ever been done as to the investigation of the
Berryphase effect on the conductionelectron wavefunction in a
system composed of a periodic array of JahnTeller 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 Berryphase connection.From a standpoint of this concept, we have succeeded in explaing the competition between the bistripe and Wignercrystallike 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 BornOppenheimer adiabatic approximation. We are going to extend our study by including nonadiabatic processes (polarons). 
Related Materials: Perovskite Manganese Oxides (Specifically, their Stripe Structures) 

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 onehalf spin, goes into the paircondensed phase as a result of the competition between the mutual Coulomb repulsions and the phonon as well as spinfluctuation mediated attractions. The physics of this chargespinphonon complex is the main themeof our research group. Specifically, we employ both the exactdiagonalization method and the Green'sfunction approach to study the electronic properties such as superconductivity, CDW, and SDW and their effects on the phonon properties in the HubbardHolstein 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 BaymKadanoff's conserving approximation leads to the exact selfenergy. Currently, we search an appropriate functional form for the selfenergy revision operator, the core of the iterative method, by investigating the exact results in smallsize systems. 
Related Materials: Organic Superconductors. CopperOxide HighTemperature Suerconductors 

Thanks to the rapid progress of computer technologies, we come to know
accurate values for the static properties of quantummechanical manybody
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 twostage theory to
obtain the vertex function: In the first stage, we have presented an algorithm
introducing "the selfenergy revision operator" which provides
the exact selfenergy as its invariant point. In the second stage, we invoke
a physicallymotivated 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 exchangecorrelation factor, a key quantity to the timedependent densityfunctional 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 exchangecorrelation 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. TwoDimensional Electron Systems at the SemiconductorInsulator Interface and the QuasiTwoDimensional Electron System in Graphite in Strong Magnetic Fields. 

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 lowtemperature
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 parahydrogen and orthodeuterium, using the pathintegral 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 UltraHigh Pressures. ElectronHole and Exciton Systems in Degenerate Semiconductors. 