# Welcome to Todo Group

## Computational Exploration of Quantum Many-body Phenomena

By solving the many-body Schrödinger equation and finding the partition function in statistical mechanics, one can know the state of matter. However, even with modern supercomputers' computing power, finding the exact solution is still impossible. It is crucial in computational physics to re-express the simulation in a simple form without losing the essential physical properties, such as symmetries and quantum correlations.

In our research group, we make full use of sampling techniques such as the Monte Carlo method, expression of quantum fluctuations based on the path integrals, information compression by singular-value decomposition and tensor network, statistical machine learning, etc. We aim to elucidate the states of matter, phase transition phenomena, and dynamics of various quantum many-body systems, from quantum spin systems to real materials. Furthermore, we study the theory of quantum computers and quantum machine learning algorithms and develop and publish open-source software for next-generation simulations.

## Seminars

- StatPhys Seminar @ UTokyo Hongo
- Computational Science Forum

## Research Highlights

- Publication List of Todo Group (2002-)

## Crystal structure prediction by combined optimization of experimental data and first-principles calculation

Crystal structure prediction has been known as one of the most difficult problems, and various prediction methods have been developed so far. Recently, joint optimization of experimental data and the theoretical potential energy calculation has been proposed. In that method, a combined cost function, a sum of reproducibility of experimental data and the potential energy, are optimized. However, combined cost function loses the information of the local minima of each cost functions. We developed a new optimization algorithm, Combined Optimization Method (COM), to overcome this difficulty. For example, it is known that the determination of crystal structure for SiO2 systems is quite difficult due to the existence of a lot of local minimum arrangements. By using the COM, we confirmed that the success rate of crystal structure prediction increases significantly.

- Naoto Tsujimoto, Daiki Adachi, Ryosuke Akashi, Synge Todo, Shinji Tsuneyuki,
*Crystal structure prediction supported by incomplete experimental data,*Phys. Rev. Materials**2**, 053801 (2018). (preprint: arXiv:1705.08613)

## Non-ergodicity in Classical Harmonic Oscillator System

Unlike the normal Langevin equation, the generalized Langevin equation, which deals with the memory effects, shows various type diffusions depending on the memory function. Recently, the anomalous diffusion and the non-ergodicity have been actively studied in the terms of the generalized Langevin equation. There are, however, some confusions in the definition of the ergodicity and there are few analysis using physical models. We propose a new non-ergodic model, which consists of harmonic oscillators, and analyze the model by the molecular dynamics, the exact diagonalization, and the analytical solution. We also reconsider the definition of the ergodicity, and clarify that the non-ergodicity observed in our model is caused by the localized mode.

- Fumihiro Ishikawa, Synge Todo,
*Localized Mode and Nonergodicity of a Harmonic Oscillator Chain,*preprint: arXiv:1805.02923.

## Machine learning for molecular dynamics with strongly correlated electrons

Machine learning (ML) is emerging as a promising tool to help model various types of many-body phenomena. A promising research area is the molecular dynamics (MD) of strongly correlated electron materials. While quantum MD methods based on the density functional theory have been successfully applied to a wide variety of materials, they have limited validity in their treatment of electron correlations. On the other hand, most of the many-body techniques, such as the dynamical mean-field theory, are computationally too costly for MD simulations. We showed that ML can be effective for building fast, linear-scaling MD potentials that capture correlated electron physics. Specifically, we used ML to enable large-scale Gutzwiller MD simulations of a liquid Hubbard model and studied the Mott metal-insulator transition. For the systems considered in the present study, ML is up to 6 orders of magnitude faster than direct quantum calculations. Our work opens a path toward a large-scale dynamical simulation of realistic models of correlated materials.

- Hidemaro Suwa, Justin S. Smith, Nicholas Lubbers, Cristian D. Batista, Gia-Wei Chern, and Kipton Barros
*Machine learning for molecular dynamics with strongly correlated electrons*

Phys. Rev. B**99**, 161107(R) (2019). (preprint: arXiv:1811.01914)