"Research for the Future Program"

1.Research Institution | The University of Tokyo | |

2.Research Area | Physical and Engineering Sciences | |

3.Research Field | Computational Science and Engineering | |

4.Term of Project | FY 1997 〜 FY 2001 | |

5.Project Number | 97P01103 | |

6.Title of Project | Material Science Simulation for Future Electronics |

Name | Institution,Department | Title of Position |

Masatoshi Imada | The University of Tokyo, Institute for Solid State Physics | Professor |

**8.Core Members**

Names | Institution,Department | Title of Position |

Hajime Takayama | The University of Tokyo, Institute for Solid State Physics | Professor |

Shinji Tsuneyuki | The University of Tokyo, Institute for Solid State Physics | Associate Professor |

Noriaki Hamada | Tokyo University of Sciense, Faculty of Science and Tehnology | Professor |

**9.Summary of Research Results**

Through the materials simulation project, we have made progress in various aspects of developing efficient algorithms and applying them to long-standing challenge in many-electron problems of computational condensed matter research. In particular, algorithms for correlated electrons and complex systems have been the main subject of this project, the main achievement is summarized in the following: (1) Exchange Monte Carlo methods have been proposed, and applied to treating slow relaxation processes and have clarified unusual critical phenomena of spin glasses. This method has also been applied in other fields such as folding of proteins. (2) Path-integral renormalization group method has been proposed and has enabled us to treat difficult problems such as correlated electron systems with geometrical frustration. This algorithm has also been applied to nuclear physics problems.(3)Algorithms for treating complexity such as interplay of orbital and spin degrees of freedom have been proposed and applied. Electron differentiation in momentum space and generation of hierarchy structure have been revealed by an improved quantum Monte Carlo method. (4) Correlator projection method has been invented and applied with a successful reproduction of electron differentiation on the verge of metal-insulator transitions.(5) First principles path-integral molecular dynamics method has been developed to consider quantum effects of light atoms and has given insights on of hydrogen phase diagram under high pressure as well as behaviors of myuonium and hydrogen in solids.(6) Polynomial expansion method has been invented and developed to treat electrons coupled to classical degrees of freedom.(7)The method, particularly the GW method, to implement correlation effects in first principles calculations have been developed and applied to total energy calculations and single particle spectra with self-energy corrections. (8)Algorithms to implement electron correlation effects in the first principles method by taking FLEX approximations have enabled to discuss magnetic and superconducting transitions. (9)Efficiency of transcorrelated method has been examined for correlated electrons.(10) Time dependent local density approximation has been developed for nonequilibrium phenomena.(11)New aspects of quantum phase transitions induced by randomness have been clarified by large-scale applications of continuous-time loop algorithm for quantum Monte Carlo simulations.By using these developed algorithms, we have predicted existence of new states of matter, and revealed various novel properties.Examples are, prediction of quantum spin liquid phase near metal-insulator phase boundary. Ordering emerging from disorder effects in quantum spins, numerical evidence for the existence of chairal spin glass in 3D systems, electron differentiation in the momentum space, and localization of light atoms by quantum zero-point motion. Those achievements have been published in 98 original papers and 40 invited talks in international conferences. |

**10.Key Words**

(1)quantum simulation、(2)strongly correlated electron systems、(3)quantum many-body problem

(4)materials design、(5)slow relaxation、(6)first-principles calculation

(7)electronic states、(8)quantum Monte Carlo method、(9)path-integral simulation