Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical review appearing in the proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri sul Mare (Salerno, Italy, October 2004

Long-distance entanglement and quantum teleportation in coupled cavity arrays

We introduce quantum spin models whose ground states allow for sizeable entanglement between distant spins. We discuss how spin models with global end-to-end entanglement realize quantum teleportation channels with optimal compromise between scalability and resilience to thermal decoherence, and can be implemented straightforwardly in suitably engineered arrays of coupled optical cavities.Comment: 4 pages, 5 figures. To appear in Phys. Rev. A (Rapid Communication

Theory of warm ionized gases: equation of state and kinetic Schottky anomaly

Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.Comment: 7 pages, 4 figures, replaced with published versio

Quantum localization and bound state formation in Bose-Einstein condensates

We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally excited state of the lowest energy band. We establish the conditions under which the presence of the upper energy bands can be neglected, determine the successive stages and the quantum phase boundaries at which localization occurs, and discuss schemes to detect it experimentally by visibility measurements. The discussed mechanism is a particular type of quantum localization that is intuitively understood in terms of the interplay between nonlinearity and a bounded energy spectrum.Comment: 6 pages, 5 figure

Modular Entanglement

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and non-interacting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.Comment: 4 pages, 6 figure

Probing Quantum Frustrated Systems via Factorization of the Ground State

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.Comment: 4 pages, 2 figures. Replaced with published versio

Transitory Inhibition of the left anterior intraparietal sulcus impairs joint actions: a continuous Theta-Burst stimulation study

Although temporal coordination is a hallmark of motor interactions, joint action (JA) partners do not simply synchronize; they rather dynamically adapt to each other to achieve a joint goal. We created a novel paradigm to tease apart the processes underlying synchronization and JA and tested the causal contribution of the left anterior intraparietal sulcus (aIPS) in these behaviors. Participants had to synchronize their congruent or incongruent movements with a virtual partner in two conditions: (i) being instructed on what specific action to perform, independently from what action the partner performed (synchronization), and (ii) being instructed to adapt online to the partner's action (JA). Offline noninvasive inhibitory brain stimulation (continuous theta-burst stimulation) over the left aIPS selectively modulated interpersonal synchrony in JA by boosting synchrony during congruent interactions and impairing it during incongruent ones, while leaving performance in the synchronization condition unaffected. These results suggest that the left aIPS plays a causal role in supporting online adaptation to a partner's action goal, whereas it is not necessarily engaged in social situations where the goal of the partner is irrelevant. This indicates that, during JAs, the integration of one's own and the partner's action goal is supported by aIPS

Hyperuniformity Order Metric of Barlow Packings

The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric $\bar{\Lambda}$. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity which involves the suppression of scattering up to a wavevector $K$. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on $K$ for all Barlow packings. We compute $\bar{\Lambda}$ for the aforementioned three classes of Barlow packings and find that to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the $\bar{\Lambda}$ of all Barlow packings is primarily controlled by the local cluster geometry. These results indicate the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.Comment: 13 pages, 7 figure

Time evolution of one-dimensional Quantum Many Body Systems

The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.Comment: Contribution for the conference proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors" held in Vietri sul Mare (Salerno, Italy) in October 200

Fuel Retention Improvement at High Temperatures in Tungsten-Uranium Dioxide Dispersion Fuel Elements by Plasma-Spray Cladding

An investigation was undertaken to determine the feasibility of depositing integrally bonded plasma-sprayed tungsten coatings onto 80-volume-percent tungsten - 20-volume-percent uranium dioxide composites. These composites were face clad with thin tungsten foil to inhibit uranium dioxide loss at elevated temperatures, but loss at the unclad edges was still significant. By preheating the composite substrates to approximately 3700 degrees F in a nitrogen environment, metallurgically bonded tungsten coatings could be obtained directly by plasma spraying. Furthermore, even though these coatings were thin and somewhat porous, they greatly inhibited the loss of uranium dioxide. For example, a specimen that was face clad but had no edge cladding lost 5.8 percent uranium dioxide after 2 hours at 4750 dgrees F in flowing hydrogen. A similar specimen with plasma-spray-coated edges, however, lost only 0.75 percent uranium dioxide under the same testing conditions