The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

Physical Review B

The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

/pdf/structural-properties-of-nanoclusters-energetic-56vj4t3ucw.pdf

Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects

The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material, as well as graphene-based spintronic devices Here we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin-orbit coupling and spin relaxation in graphene Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other 2D materials

Graphene Spintronics

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Electronic Transport In Mesoscopic Systems

We study the transverse electron focusing in a two-dimensional electron gas with Rashba spin-orbit coupling. We show that the interplay between the external magnetic field and the spin-orbit coupling gives two branches of states with different cyclotron radius within the same energy window. This effect generates a splitting of the first focusing peak in two contributions. Each one of these contributions is spin polarized. The surface reflection mixes the two branches and the second focusing peak does not present the same effect. While for GaAs/ AlGaAs heterostructures the effect is small, in systems like InSb/ InAlSb the effect should be clearly observed.

Transverse electron focusing in systems with spin-orbit coupling

Phonon engineering with acoustic nanocavities: Theoretical considerations on phonon molecules, band structures, and acoustic Bloch oscillations

Bose-Glass Phase in Twinned YBa 2 Cu 3 O 7-δ

We study Josephson junctions (JJs) in which the region between the two superconductors is a multichannel system with Rashba spin-orbit coupling (SOC) where a barrier or a quantum point contact (QPC) is present. These systems might present unconventional Josephson effects such as Josephson currents for zero phase difference or critical currents that depend on the current direction. Here, we discuss how the spin polarizing properties of the system in the normal state affect the spin characteristics of the Andreev bound states inside the junction. This results in a strong correlation between the spin of the Andreev states and the direction in which they transport Cooper pairs. While the current-phase relation for the JJ at zero magnetic field is qualitatively unchanged by SOC, in the presence of a weak magnetic field, a strongly anisotropic behavior and the mentioned anomalous Josephson effects follow. We show that the situation is not restricted to barriers based on constrictions such as QPCs and should generically arise if in the normal system the direction of the carrier's spin is linked to its direction of motion.

Spin-orbit induced chirality of Andreev states in Josephson junctions

Using an extensive scaling analysis of the transport properties in twinned YBaCuO(123) crystals we have experimentally found the predicted change in the universality class of the Bose-glass to liquid transition when the magnetic field is applied at small angles away from the direction of the correlated defects. The new dynamical critical exponent is s'=1.1 +/-0.2.

http://arxiv.org/pdf/cond-mat/9806376.pdf

C. A. Balseiro

Papers

Transverse electron focusing in systems with spin-orbit coupling

Phonon engineering with acoustic nanocavities: Theoretical considerations on phonon molecules, band structures, and acoustic Bloch oscillations

Bose-Glass Phase in Twinned YBa 2 Cu 3 O 7-δ

Spin-orbit induced chirality of Andreev states in Josephson junctions

The Bose-glass phase in twinned YBaCuO(123)