Quasi-pinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank-eight approximation we find well-defined families of saturation conditions.Comment: 22 pages, 6 figures, minor changes, references adde

Relating correlation measures: the importance of the energy gap

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H$_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.Comment: 6 pages, 3 figure

Orbital-Free Quasi-Density Functional Theory

Wigner functions are broadly used to probe non-classical effects in the macroscopic world. Here we develop an orbital-free functional framework to compute the 1-body Wigner quasi-probability for both fermionic and bosonic systems. Since the key variable is a quasi-density, this theory is particularly well suited to circumvent the problem of finding the Pauli potential or approximating the kinetic energy in orbital-free density functional theory. As proof of principle, we find that the universal functional for the building block of optical lattices results from a translation, a contraction, and a rotation of the corresponding functional of the 1-body reduced density matrix, indicating a strong connection between these functional theories. Furthermore, we relate the concepts of Wigner negativity and $v$-representability, and find a manifold of ground states with negative Wigner functions.Comment: 7 pages, 6 figure

On the symmetry of the Quadratic Assignment Problem through Elementary Landscape Decomposition

When designing meta-heuristic strategies to optimize the quadratic assignment problem (QAP), it is important to take into account the specific characteristics of the instance to be solved. One of the characteristics that has been pointed out as having the potential to affect the performance of optimization algorithms is the symmetry of the distance and flow matrices that form the QAP. In this paper, we further investigate the impact of the symmetry of the QAP on the performance of meta-heuristic algorithms, focusing on local search based methods. The analysis is carried out using the elementary landscape decomposition (ELD) of the problem under the swap neighborhood. First, we study the number of local optima and the relative contribution of the elementary components on a benchmark composed of different types of instances. Secondly, we propose a specific local search algorithm based on the ELD in order to experimentally validate the effects of the symmetry. The analysis carried out shows that the symmetry of the QAP is a relevant feature that influences both the characteristics of the elementary components and the performance of local search based algorithms.IT1244-19, PID2019-106453GA-I00/AEI/10.13039/501100011033, H202