Development of first principles based calculation methodologies for correlated systems

Abstract

In this thesis, we will introduce a study of a computational methodology based on the first principles. Throughout the thesis, the method of obtaining spin-spin interaction strength by a linear response theory, and a method of imaginary Green's function analytic continuation through machine-learning will be presented. First, we investigated the reliability and applicability of so-called magnetic force linear response method to calculate spin-spin interaction strengths from first-principles. We examined the dependence on the numerical parameters including the number of basis orbitals and their cutoff radii within nonorthogonal LCPAO (linear combination of pseudo-atomic orbitals) formalism. It is shown that the parameter dependence and the ambiguity caused by these choices are small enough in comparison to other computation approach and experiments. Further, we tried to pursue the broader applicability of this technique. We showed that magnetic force theory can provide the reasonable prediction especially for the case of strongly localized moments even when the ground state configuration is unknown or the total energy value is not accessible. The formalism is extended for LCPAO to carry the orbital resolution from which the matrix form of the magnetic coupling constant is calculated. From the applications to Fe-based superconductors including LaFeAsO, NaFeAs, $BaFe_2As_2$ and FeTe, the distinctive characteristics of orbital-resolved interactions are clearly noticed in between single-stripe pnictides and double-stripe chalcogenides.

Second, we presented a machine learning (ML) approach to the analytic continuation which is the notorious problem in quantum many-body physics. Especially analytic continuation is applied to obtain the density of states (DOS) from imaginary time Green's function calculated from quantum Monte Carlo (QMC). However, the analytic continuation is an ill-conditioned problem. Therefore, many numerical approaches exist

such as maximum entropy method, stochastic method, and Pade’ approximation. Here we show that using modern machine learning techniques, such as convolutional neural network and stochastic gradient descent based optimizers, ML-based Green's function to DOS kernel can be realized without detailed “domain-knowledge” about previous analytic continuation approaches. Furthermore, the ML-based kernel is faster than conventional analytic continuation algorithms and more robust to noise from Green’s function. Our approach to tackling ill-posed problems by data-based ML shows the applicability of ML in other ill-posed problems.