Related papers: Expectation values of single-particle operators in…
A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor,…
We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random…
As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
We show how the use of variational states to approximate the ground state of a system can be employed to study a multi-mode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity,…
With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Recently, it has been shown that the ground-state energy of a quantum many-body system can be written in terms of cumulants. In this paper we show that the energies of excited states can be expressed similarly. These representations are…
We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including P- and P,T-odd terms for the BaF molecule. The ground state wave function of BaF molecule is found with the help of the Relativistic…
Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for…
We construct superposition states of energy eigenstates of the hydrogen molecule using classically emulated digital quantum simulation. We generate the ground state and excited states of the system via the twirling operation method, and…
A microscopic formalism is developed that includes the coupling to two particle-hole phonons in the particle-hole propagator by extending the dressed random phase approximation (DRPA) equation for a finite system. The resulting formalism is…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
The effects of the correlations in the ground state of $^{16}$O on the octupole and dipole excitations are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. It is found that…
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…
This chapter gives an introduction to qualitative and quantitative topological analyses of molecular electronic transitions. Among the possibilities for qualitatively describing how the electronic structure of a molecule is reorganized upon…
Rescattering electrons offer great potential as probes of molecular properties on ultrafast timescales. The most famous example is molecular tomography, in which high harmonic spectra of oriented molecules are mapped to ``tomographic…
Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle-particle random phase approximation (ppRPA) as…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…