Research Interests

The main focus of my research is to describe the electron correlation effects in the condensed matters from the theoretical point of view. So far, I have developed a new path-integral theory which is free from Grassmann algebra and applicable for spectroscopy, such as photoemission, light absorption, and x-ray scattering. The strong coupling between the spin and charge excitations, inherent in the strongly correlated electron systems, are clarified through the numerical calculations of these spectra. I have also developed a resonating Hartree-Fock method to describe the quantum fluctuations in the strongly correlated electron systems. More information is given below.

1. Path-integral theory for the optical response functions

In the path-integral theory, the two-body Coulomb interaction is reduced into the linear interaction between an electron and scaler boson field. As a result, we can easily diagonalize such a one-body Hamiltonian once a configuration of bonson fields is determined. However, the possible number of the configurations is so huge that we cannot completely sum them up. (Note that the summation over the configurations of boson fields corresponds to the path-integration.) Therefore, we estimate this summation by means of the Monte Carlo simulation.

The merit of this mehod lies in the easy access to the spectroscopy, such as photoemission, light absorption and emission. We can calculate the spectral functions almost exactly even for the strongly correlated electrons systems. So far, we have successfully described the experimentally observed photoemission spectra of the one-dimensional Cu-oxides and halogen-bridged Ni complex within the framework of the Hubbard and extended Hubbard models, respectively.

One important result obtained by this path-integral approach is that the photoemission spectrum of the strongly correlated electron system is predominated by the incoherent component caused by the nonlinear coupling between the photo-generated hole and magnetic fluctuations. We reached this important result in the following. First, we calculated a photoemission spectrum for the electron system having the gap in the magnetic excitatiion. In such a sytem, we can clearly distinguish a sharp magnon-free
(coherent) peak and broad magnon-coupled (incoherent) component because of the finite magnon gap. Then, by tracing the magnon gap-dependence of the coherent peak, we can clearly conclude that the the photoemission spectrum consists of  the multi-magnon incoherent component almost completely.

On the other hand, in the weakly correlated electron system, the photoemission spectrum still has a coherent component near the Fermi energy. We are now trying to establish this result and also to clarify the mechanism of the metal-insulator transition in the weakly correlated electron system.

2. Resonating Hartree-Fock theory for quantum fluctuations

We all know that Hartree-Fock theory no longer works well on the strongly interacting electron system. Theorists have tried to descirbe the electron correlations beyond a Hartree-Fock state. The exact diagonalization method is the most straightforward approach to explain the electron correlation completely. However, this method is applicable only for the samll systems up to about 24 electrons. The quantum Monte Carlo method is another strong approach accessible to more than 100 electrons. However, the quantum Monte Carlo method has a drawback called the negative sign problem. The probability to update the configuration becomes negative when the electron-hole symmetry is broken. As a result, we cannot make an importance sampling and get accurate observavles. For example, we cannot access to the doped systems by the quantum Monte Carlo method. Density matrix renormalization group (DMRG) method is also a powerful approach accessible to the almost inifinite systems. However, the DMRG method is accessible only to the one-dimensional system.

The resonating Hartree-Fock method was originally developed by H. Fukutome to descirbe both the electron correlations and quantum fluctautions. These two concepts are of-course closely related, but the previous theories cannot even suggest how they are. This method constructs a many-body wave function by superposition of non-orthogonal Slater deteminants (S-dets), such as


Here, not only the superpostion coefficients C's but also the molecular orbitals in all the S-dets are variational determined. The orbital optimization is very time-consuming, but makes the wave function much better than the simple superposition without the orbital optimization. It was shown for the one-dimensional Hubbard model that the resonating Hartree-Fock wave function describe the more correlation energies than the well-established variational Monte Carlo method.

The most important merit to employ the resonating Hartree-Fock method is that we can direclty obtain information on quantum fluctuations through the S-dets constituting the wave function. For example, in the one-dimensional Hubbard system, the Hartree-Fock ground state is a spin density wave, where the energy is degenerate for the spin density alternations up down up down ..., and down up down up ... .In such a broken symmetry state, we have a low energy excitation connecting the two degenated alternating phases called a soliton. Then, we showed for the one-dimensional Hubbard system, the dominant quantum fluctuations are described as a translational, vibrational and breathing motions. Furhtermore, we also clarified that in the spin density wave-charge density wave phase transition, the domain wall connecting the two sates workd as precursor of the quantum nucleation.

The resonating Hartree-Fock method is thus a very promissing approach to describe the electron correlation effects quite efficiently. I am now trying to extend this method to the spectroscopy.