## Theory of quantum many-body systems

We theoretically study physics of quantum many-body (QMB) systems, in which constituents obey the laws of the quantum mechanics. Examples include electrons in solids, liquid helium, ultracold gases, and quantum computers. In QMB systems, many counter-intuitive phenomena emerge thanks to the cooperation/competition of quantum effects and interparticle interactions. Specifically, we are interested in superfluidity, superconductivity, supersolidity, Kondo effects, quantum magnetism, quantum phase transitions, non-equilibrium dynamics, many-body localization, etc.

One of the severest difficulties in theoretical analyses of QMB systems lies in the fact that the numerical cost for describing a QMB system grows in general exponentially with the size of the system. Hence, in order to perform numerical analyses of realistic experiments of a QMB system, one needs efficient theoretical/numerical methods that circumvent such exponential growth of the numerical cost. We utilize and develop several numerical methods for QMB systems, such as matrix product states, cluster mean-field theory, and truncated Wigner approximation.

In recent years, analog quantum simulation has attracted much attention as a new tool for studying QMB physics. A quantum simulator mimics complex phenomena emerging in a real material by using an artificial QMB system with high controllability, including ultracold gases and trapped ions. We strongly support development/invention of quantum simulators in some experimental groups from a theoretical standpoint.

### Ongoing projects

Research title | Program title | Sponsor | Term | Amount (K JPY) | Role |

Novel quantum many-body phenomena pioneered by means of tensor-network methods and quantum simulators | FOREST | JST | Apr. 2021 – Mar. 2023 | 20,000 | PI |

Experimental study of open quantum many-body systems using strongly-correlated cold atomic gases | KAKENHI KIBAN (B) | JSPS | Apr. 2021 – Mar. 2023 | 1,400 | Collaborator |

Development of cold-atom quantum simulators on the basis of spatio-temporal optical control at the attosecond-nanometer level and its application to quantum computations | Q-LEAP Flagship program Fundamental research | MEXT | Nov. 2019 ~ Mar. 2029 | 25,400 | Collaborator |

### Projects in the past

Pioneering novel quantum many-body physics with orbital and spin degrees of freedom of ultracold gases in optical lattices | KAKENHI KIBAN (S) | JSPS | Jul. 2018 ~ Mar. 2023 | 15,000 | Collaborator |

Developing innovative optical-lattice quantum simulators on the basis of high controllability of ultracold gases | CREST | JST | Oct. 2016 ~ Mar. 2022 | 26,200 | Collaborator |

Realizing quantum gravity with both holographic principle and ultracold gases in optical lattices | KAKENHI KIBAN (C) | JSPS | Apr. 2018 ~ Mar. 2021 | 3,300 | PI |

Novel quantum phases pioneered by ultimate control and observation of Ytterbium quantum gases | KAKENHI KIBAN (S) | JSPS | Jul. 2013 ~ Mar. 2018 | 4,000 | Collaborator |

Quantum phase transitions and non-equilibrium dynamics of one-dimensional quantum fluid in non-uniform potentials | KAKENHI KIBAN(C) | JSPS | Apr. 2013~Mar. 2016 | 2,900 | PI |

Dynamics of strongly correlated Bose gases in optical lattices | RIKEN SPR’s Funding | RIKEN | Apr. 2010 ~ Sep. 2012 | 3,000 | PI |

Realizing quantum Fermi-Pasta-Ulam recurrence with ultracold gases | KAKENHI Start-up | JSPS | Aug. 2010~ Mar. 2011 | 1,250 | PI |

Breakdown of superflow in Bose gases in optical lattices | KAKENHI JSPS fellow’s funding | JSPS | Apr. 2008 ~ Mar. 2010 | 1,600 | PI |

Spontaneous symmetry breaking and elementary excitations in Bose-Einstein condensed systems | KAKENHI JSPS fellow’s funding | JSPS | Apr. 2005 ~ Mar. 2008 | 2,700 | PI |