# Research themes¶

## First-Principles Quantum Monte Carlo simulations¶

The behavior of “electrons”, which govern the chemical/physical properties of a material, can be predicted by solving the Schrödinger equation. This equation is usually solved numerically through first-principles calculations. At present, the most popular first-principles calculation is based on the wavefunction theory (WFT) or the density functional theory (DFT), which have achieved great success in the field of material science/condensed matter physics. There is, however, still serious drawbacks; for example, in DFT calculations, the choice of exchange-correlation functional significantly affects the results, which can sometimes lead to a quantitatively wrong prediction.

First-principles quantum Monte Carlo (QMC) is an alternative framework to tackle the solution of the many-body Schrödinger equation by means of a stochastic approach. This framework is expected to form the next generation of electronic structure calculations because it can directly handle a many-body wave function and because it does not rely on exchange-correlation functionals. The development of large parallel computers in the 21st century has greatly alleviated the “statistical error problem”, which is a fundamental drawback associated with the use of the Monte Carlo method. Thus, practical applications of this framework have multiplied. A development race has begun around the world, because the algorithm has good compatibility with exascale supercomputers.

I am one of the developers of a SISSA quantum Monte Carlo package, called TurboRVB. This package was initially launched by Prof. Sandro Sorella (International School for Advanced Studies/Italy) and Dr. Michele Casula (Sorbonne University/France) and has been continuously developed by many researchers for over 20 years through international collaborations.

TurboRVB is distinguishable from other QMC codes in the following features:

The code employs a resonating valence bond (RVB)-type wave function, such as the Jastrow Geminal/Jastrow Pfaffian. This wave function includes the correlation effect beyond the Jastrow-Slater wave function, which is commonly used in other QMC codes.

Implemented state-of-art optimization algorithms, such as the stochastic reconfiguration and the linear method, realize a stable optimization of the amplitude and nodal surface of many-body wave functions at the variational quantum Monte Carlo level.

The code implements the so-called lattice regularized diffusion Monte Carlo method, which provides a numerically stable diffusion quantum Monte Carlo calculation.

The implementation of an adjoint algorithmic differentiation allows us to differentiate many-body wave functions efficiently and to perform structural optimizations and calculate molecular dynamics.

We are now promoting further applications of the software in the field of materials science/condensed matter physics by exploiting the above features.

## Applications of first-principles calculations¶

The materials informatics (MI) paradigm has recently attracted much attention. It stimulates researchers to try to use high-throughput first-principle calculations for designing a novel material. However, computational physics and chemistry have originally been used for revealing mechanisms so far, which is still a valid strategy for designing a novel material. I am applying first-principle calculations to compounds recently synthesized by experimental groups.

### Novel superconductors in layered titanium-oxypnictides¶

Almost all metals show zero resistivity at very low temperature, which is called a critical temperature (T_{c}). This phenomenon was discovered in Hg by Kamerlingh Onnes in 1911 and named as “superconductivity” later. A lot of researchers have been looking for novel high-T_{c} superconductors, ultimately room-temperature superconductors. Although several high-T_{c} superconducting families have been found, no room-temperature one has been discovered so far.

I am currently developing new theories and implementations for FP-QMC, but I started my career as an experimental researcher. My supervisors (Prof. Kageyama and Dr. Yajima) gave me a mission to find a novel superconductor in titaninum compounds. Fortunately, we found several novel superconductors such as BaTi_{2}Sb_{2}O and BaTi_{2}Bi_{2}O which are categorized as layered titanium-oxypnictides. They have still been studied by many groups because their analogies of cuprates and iron-arsenides high-T_{c} superconductors. Although several experiments such as NMR and muSR had revealed the superconducting mechanism, details of structural disorders occurring at low temperature had not been detected by X-ray or neutron diffraction measurements. I applied first-principle phonon calculations to the layered titaninum-oxpnictides to reveal the low-temperature structures.

### Collaborations with experimental groups¶

I am actively collaborating with experimental groups so that I can take advantage of my experience that I belonged to an experimental group and synthesized inorganic compounds. I advise how to use a DFT code or calculate electronic and/or phonon structures by myself.

### Validation and verification of Density Functional Theory¶

Recently, the materials informatics (MI) paradigm, in which novel materials are designed or searched for using techniques of information science and/or computational physics, has attracted much attention because of rapid improvements in computer and information science (including artificial intelligence, AI). The most important problem when applying AI to the field of materials is a lack of arranged databases for physical properties and functions, which is very different situation from board games and web services. Then, high-throughput ab initio calculations of physical properties are often performed to create large-scale databases for machine learning or data mining in MI.

Density functional theory (DFT) seems a promising framework in which to perform quantitative evaluations of physical properties. It is, however, sometimes unable to reproduce experimental results owing to the limitation such as a failure to take exchange-correlation effects into account, a lack of excited-state information, or the unavailability of an appropriate model. Therefore, it is very important to investigate whether or not DFT calculation can quantitatively predict a physical property even if the method has already been implemented in a DFT code.

To validate the predictive power, we are collecting experimental data and comparing the experimental data and calculation results.