Iterative diagonalization of the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis set: Application to sp-electron systems with deep core states

Abstract

We develop an iterative diagonalization scheme in solving a one-body self-consistent-field equation in the transcorrelated (TC) method using a plane-wave basis set. Non-Hermiticity in the TC method is well handled with a block-Davidson algorithm. We verify the required computational cost is efficiently reduced by our algorithm. In addition, we apply our plane-wave-basis TC calculation to some simple sp-electron systems with deep core states to elucidate an impact of the pseudopotential approximation to the calculated band structures. We find a position of the deep valence bands is improved by an explicit inclusion of core states, but an overall band structure is consistent with a regular setup that includes core states into the pseudopotentials. This study offers an important understanding for the future application of the TC method to strongly correlated solids.

Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory

“…In a separate development, there has been renewed interest in so-called transcorrelated (TC) methods [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], based on Jastrow factorisation of the electronic wavefunction, which result in effective similarity transformed (ST) Hamiltonians [40,43]. Although TC methods were originally proposed as a way to accelerate basis set conver-gence in electronic wavefunctions, it has become apparent that such similarity transformations can also be extremely helpful in the context of strongly correlated systems.…”

Correlated Band Structure of a Transition Metal Oxide ZnO Obtained from a Many-Body Wave Function Theory

“…In addition, the correlated band structure, which is quite useful in various kinds of theoretical analyses, is not easily obtained in many WFTs. For example, calculation of the band structure in the framework of VMC or DMC requires a large number of single-point calculations of the excited states, which is a clear difference from a mean-field-like approach such as DFT, whereby the whole band structure is obtained at once.From this viewpoint, the transcorrelated (TC) method [20-23] is a fascinating WFT that can be applied to solids with reliable accuracy and moderate computational cost [24][25][26][27][28][29]. The TC method adopts the socalled Jastrow ansatz, which is based on a promising strategy often adopted in several WFTs such as QMC methods to describe strong electron correlations; i.e., the electron-electron distance is included into many-body wave functions.…”

“…From this viewpoint, the transcorrelated (TC) method [20][21][22][23] is a fascinating WFT that can be applied to solids with reliable accuracy and moderate computational cost [24][25][26][27][28][29]. The TC method adopts the socalled Jastrow ansatz, which is based on a promising strategy often adopted in several WFTs such as QMC methods to describe strong electron correlations; i.e., the electron-electron distance is included into many-body wave functions.…”

Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian

“…A recent study that combines the TC method with the quantum computational method is also promising [24]. Moreover, an efficient treatment of the correlation effects enables one to apply the TC method to solids [25][26][27][28][29], including its combination with the CI-singles [30] and the second-order MP perturbation theory [31]. The TC and related methods were also applied to the Hubbard model [32][33][34][35], electron gas [25,[36][37][38][39], one-dimensional quantum gas with contact interactions [40], and ultracold atoms [41].…”