Related papers: Revisiting the variational two-particle reduced de…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum ($J$) and projection of total angular momentum ($M_{J}$) states in atomic systems described by non-relativistic…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom. Collective modes (vibration and/or rotation) dominate…
Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave…
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational…
The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced density-matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can…
Nuclear many-body theory is based on the tenet that nuclear systems can be accurately described as collections of point-like particles. This picture, while providing a remarkably accurate explanation of a wealth of measured properties of…
A variational technique to describe the ground and scattering states below the break-up threshold for a three-nucleon system is developed. The method consists in expanding the wave function in terms of correlated Harmonic Hyperspherical…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows to obtain ground-state properties of a quantum many-body system without reference to an $N$-particle wave…
In order to extend the density-matrix renormalization-group (DMRG) method to two-dimensional systems, we formulate two alternative methods to prepare the initial states. We find that the number of states that is needed for accurate energy…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…
We describe the use of the Density Matrix Renormalization Group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results…
In this work, the reliability of the Landau expression for the nuclear level density calculations is tested, for the first-time, to describe nuclear level densities of some light, intermediate mass and heavy nuclei at excitations…
The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM)…
The properties of high-density nuclear and neutron matter are studied using a relativistic mean-field approximation to the nuclear matter energy functional. Based on ideas of effective field theory, nonlinear interactions between the fields…