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A selfconsistent many body approach for the description of gases with quartets, trions, and pairs is presented. Applications to 3D Fermi systems at low density are discussed.

The d–p band model, a periodic array of strongly correlated d states with hopping to a p band, and in the presence of a uniform applied magnetic field is studied as a function of temperature using Roth's variational method. Expanding the σ spin electron occupation numbers of d and p states to first order in the magnetic field h, we calculate the linear term of the field induced magnetization and thus the susceptibility. This is given in terms of the number of holes for La_{2 - x}Sr_xCuO₄, in the limit of strongd–d correlations and we study the role of doping x and temperature "T" on the susceptibility.

In this work the variational Roth's approach previously developed by the present authors to describe cuprate systems is extended to include the superconducting properties. We extend the Beenen and Edwards approach by including the d–p hybridization. The role of the d–p hybridization in modifying the values of superconducting order parameter is then studied in terms of the adopted values of the parameters defining the Hamiltonian of the system.

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems.

Charge-spin separation was predicted theoretically in one-dimensional strongly interacting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohm rings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation.

Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential.

These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

The Tomonaga–Luttinger–Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.

The ternary fulleride, Rb${}_{0.25}$Cs${}_{2.75}$C${}_{60}$, is the most expanded member of the family of face-centered cubic (fcc) structured superconducting fullerides ever accessed with superconductivity surviving at ambient pressure closest to the Mott insulator boundary. Here, we study the evolution of its structural and electronic properties with temperature. At ambient temperature, Rb${}_{0.25}$Cs${}_{2.75}$C${}_{60}$ lies in the Mott–Jahn–Teller (MJT) insulating part of the phase diagram. High-resolution synchrotron X-ray diffraction shows that its structure remains strictly cubic at all temperatures, but the transition to the metallic state at $\sim$ 50 K — evident in the evolution of the magnetic susceptibility with temperature — is accompanied by a lattice collapse, $\mathrm{\Delta }$V/V₀ of $-0.5\%$. Bulk superconductivity then emerges on further cooling with a T${}_c$ of 25.9 K. The results permit the extension of the electronic phase diagram of A₃C${}_{60}$ fullerides as close as possible to the metal–insulator (M–I) crossover.

The study of complex oxides and oxide heterostructures has dominated the field of experimental and theoretical condensed matter research for the better part of the last few decades. Powerful experimental techniques such as molecular beam epitaxy and pulsed laser deposition have made fabrication of oxide heterostructures with atomically sharp interfaces possible, whereas more and more sophisticated handling of exchange and correlations within first principles methods including density functional theory (DFT) supplemented with Hubbard U corrections and hybrid functionals, and beyond DFT techniques such as dynamical mean field theory (DMFT) have made understanding of such correlated oxides and oxide interfaces easier. The emergence of the high-mobility two-dimensional electron gas with fascinating properties such as giant photoconductance, large negative magnetoresistance, superconductivity, ferromagnetism, and the mysterious coexistence of the latter two have indeed caught the attention of condensed matter community at large. Similarly, strain tuning of oxides have generated considerable interest particularly after the recent discovery of piezoelectric methods of strain generation. Theoretical understanding and prediction of the possible exotic phases emerging in such complex oxides both under strain and in heterostructures will eventually lead to better design of device applications in this new emerging field of oxide electronics, along with possible discovery of exotic physics in condensed matter systems, which may be of wider significance! In this review, we briefly look at theoretical studies of novel phenomena in oxides under strain and oxide heterostructure, and try to understand the role of exchange and particularly correlation in giving rise to such exotic electronic states. This review though primarily focuses on the theoretical aspects on understanding the different mechanism of the phenomena of emergence of exotic phases, does provide a unique overview of the experimental literature as well, accompanied by the theoretical understanding such that relevant device applications can be envisaged.

Interacting bosons, fermions and Bose-Fermi mixtures in optical lattices form novel model systems for the investigation of fundamental quantum many body effects. This article summarizes some of our recent work on interacting bosonic and fermionic quantum gases in optical lattices. We show how the compressibility of a fermionic quantum gas mixture can be evaluated by measuring its size vs trap confinement. The results are compared to ab-initio Dynamical Mean Field Theory (DMFT) calculations, for which we find very good agreement with the experiment. Furthermore, quantum phase diffusion is introduced as a powerful method for the measurement of the renormalized Hubbard parameters underlying most lattice models.

Strongly correlated states in many-body systems are traditionally created using elastic interparticle interactions. Here we show that inelastic interactions between particles can also drive a system into the strongly correlated regime. This is shown by an experimental realization of a specific strongly correlated system, namely a one-dimensional molecular Tonks-Girardeau gas.

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems.

Charge-spin separation was predicted theoretically in one-dimensional strongly interacting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohm rings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation.

Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential.

These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

The Tomonaga–Luttinger–Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.