Related papers: Local Relativistic Exact Decoupling
Atom localization enables a high-precision imaging of the atomic position, which has provided vast applications in fundamental and applied science. In the present work, we propose a scheme for realizing two-dimensional off-axis atom…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to…
Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for…
A two-orbital two-electron diatomic model resembling LiH is used to investigate the differences between the exact L\"owdin-Shull and approximate Hartree-Fock-Bogoliubov and Baerends-Buijse density matrix functionals in the medium- to…
We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations…
We present an embedding approach to treat local electron correlation effects in periodic environments. In a single, consistent framework, our plane-wave based scheme embeds a local high-level correlation calculation (here Coupled Cluster…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be…
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global…
The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are…
A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically…
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real…