We study spinless fermions in a flux threaded AB$_2$ chain taking into account nearest-neighbor Coulomb interactions. The exact diagonalization of the spinless AB$_2$ chain is presented in the limiting cases of infinite or zero nearest-neighbor Coulomb repulsion for any filling. Without interactions, the AB$_2$ chain has a flat band even in the presence of magnetic flux. We show that the respective localized states can be written in the most compact form as standing waves in one or two consecutive plaquettes. We show that this result is easily generalized to other frustrated lattices such as the Lieb lattice. A restricted Hartree-Fock study of the $V/t$ versus filling phase diagram of the AB$_2$ chain has also been carried out. The validity of the mean-field approach is discussed taking into account the exact results in the case of infinite repulsion. The ground-state energy as a function of filling and interaction $V$ is determined using the mean-field approach and exactly for infinite or zero $V$. In the strong-coupling limit, two kinds of localized states occur: one-particle localized states due to geometry and two-particle localized states due to interaction and geometry. These localized fermions create open boundary regions for itinerant carriers. At filling $\rho=2/9$ and in order to avoid the existence of itinerant fermions with positive kinetic energy, phase separation occurs between a high-density phase ($\rho=2/3$) and a low-density phase ($\rho=2/9$) leading to a metal-insulator transition. The ground-state energy reflects such phase separation by becoming linear on filling above 2/9. We argue that for filling near or larger than 2/9, the spectrum of the t-V AB$_2$ chain can be viewed as a mix of the spectra of Luttinger liquids (LL) with different fillings, boundary conditions, and LL velocities.Comment: 17 pages, 17 figure

The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systematic analysis. Early investigations have found evidence that these constraints are exactly saturated in several physically relevant systems; e.g. in a certain electronic state of the Beryllium atom. It has been suggested that in such cases, the constraints, rather than the details of the Hamiltonian, dictate the system's qualitative behavior. Here, we revisit this question with state-of-the-art numerical methods for small atoms. We find that the constraints are, in fact, not exactly saturated, but that they lie much closer to the surface defined by the constraints than the geometry of the problem would suggest. While the results seem incompatible with the statement that the generalized Pauli constraints drive the behavior of these systems, they suggest that the qualitatively correct wave-function expansions can in some systems already be obtained on the basis of a limited number of Slater determinants, which is in line with numerical evidence from quantum chemistry.

We study a two terminal electronic conductance through an AB2 ring which is an example of the family of itinerant geometrically frustrated electronic systems. These systems are characterized by the existence of localized states with nodes in the probability density. We show that such states lead to distinct features in the conductance. For zero magnetic flux, the localized states act as a filter of the zero frequency conductance peak, if the contact sites have hopping probability to sites which are not nodes of the localized states. For finite flux, and in a chosen orthonormal basis, the localized states have extensions ranging from two unit cells to the complete ring, except for very particular values of magnetic flux. The conductance exhibits a zero frequency peak with a dip which is a distinct fingerprint of the variable extension of these localized states.

The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighborhood of active orbitals around the Fermi level. The respective wavefunction ansatzes which involve all possible electron configurations of active orbitals can be characterized by the saturation of a certain number of Pauli constraints   n 0 1 i , identifying the occupied core orbitals (n i =1) and the inactive virtual orbitals (n j =0). In Part I, we generalize this crucial concept of active spaces by referring to the generalized Pauli constraints. To be more specific, we explain and illustrate that the saturation of any such constraint on fermionic occupation numbers characterizes a distinctive set of active electron configurations. A converse form of this selection rule establishes the basis for corresponding multiconfigurational wavefunction ansatzes. In Part II, we provide rigorous derivations of those findings. Moroever, we extend our results to non-fermionic multipartite quantum systems, revealing that extremal single-body information has always strong implications for the multipartite quantum state. In that sense, our work also confirms that pinned quantum systems define new physical entities and the presence of pinnings reflect the existence of (possibly hidden) ground state symmetries.

The transport of fermions through nanocircuits plays a major role in mesoscopic physics. Exploring the analogy with classical wave scattering, basic notions of nanoscale transport can be explained in a simple way, even at the level of undergraduate Solid State Physics courses, and more so if these explanations are supported by numerical simulations of these nanocircuits. This paper presents a simple tight-binding method for the study of the conductance of quantum nanorings connected to one-dimensional leads. We show how to address the effects of applied magnetic and electric fields and illustrate concepts such as Aharonov-Bohm conductance oscillations, resonant tunneling and destructive interference.