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 show that in a two dimensional electron gas (2DEG) the interplay between the Rashba spin-orbit coupling and a potential barrier (eg., the sample edge) generates interesting spin effects. In the presence of an external charge current, a spin accumulation is built up near the barrier while in equilibrium there is an inhomogeneous spin current which is localized at the barrier and flows parallel to it. When an in-plane magnetic field perpendicular to the barrier is applied, the system also develops an inhomogeneous charge current density. These effects originate purely from the structure of the eigenstates near the boundary.

https://arxiv.org/pdf/cond-mat/0405065.pdf

Spin Accumulation and Equilibrium Currents at the Edge of 2DEGs with Spin-Orbit Coupling

We study the influence of defects on the structure of the order parameter for a ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$ superconductor. Using a Ginzburg-Landau theory which couples the d-wave and s-wave components of the order parameter, we show that in the vicinity of defects there is an induced s-wave pairing that extends up to a length scale given by the coherence length. We present results for columnar defects along different directions, twin boundaries, and point defects. \textcopyright{} 1996 The American Physical Society.

Ginzburg-Landau theory of defects in d-wave superconductors.

Transport measurements in the mixed state of oxygen-deficient YBa 2 Cu 3 O 7−δ single crystals using the flux transformer configuration show that the flux liquid changes with increasing anisotropy from strongly correlated to uncorrelated in the field direction. For intermediate coupling, the current inducing loss of vortex correlation has a maximum near the irreversibility temperature. Thus, an effective softening of vortex lines with decreasing temperature is detected. We propose a simple model that accounts for this behavior by including the effects of the pinning potential on the dynamics of vortices.

Dynamic softening of vortex lines in YBa2Cu3O7−δ single crystals

We analyze the origin of spin-orbit coupling (SOC) in fluorinated graphene using density functional theory (DFT) and a tight-binding model for the relevant orbitals. As it turns out, the dominant source of SOC is the atomic spin-orbit of fluorine adatoms and not the impurity-induced SOC based on the distortion of the graphene plane as in hydrogenated graphene. More interestingly, our DFT calculations show that SOC is strongly affected by both the type and concentrations of the graphene's carriers, being enhanced by electron doping and reduced by hole doping. This effect is due to the charge transfer to the fluorine adatom and the consequent change in the fluorine-carbon bonding. Our simple tight-binding model, which includes the SOC of the $2p$ orbitals of F and effective parameters based on maximally localized Wannier functions, is able to account for the effect. The strong enhancement of the SOC induced by graphene doping opens the possibility to tune the spin relaxation in this material.

Gate-induced enhancement of spin-orbit coupling in dilute fluorinated graphene

During the last years there has been much interest, and theoretical discussion, about the possibility to use spin–orbit coupling to control the carriers spins in two-dimensional semiconducting heterostructures. Spin polarization at the sample edges may occur as the response of systems with strong SO-coupling to an external transport current, an effect known as spin Hall effect. Here, we show that in a 2DEG with Rashba SO-coupling, spin polarization near the sample edge can develop kinematically for low electron densities. We also discuss the effect in quantum wires where lateral confinement plays an important role.

https://fisica.cab.cnea.gov.ar/solidos/personales/usaj/mypdf/Reynoso2006a%20-%20Charge%20and%20spin%20transport%20in%20nanoscopic%20structures%20with%20spin_textendashorbit%20coupling.pdf

C. A. Balseiro

Papers

Spin Accumulation and Equilibrium Currents at the Edge of 2DEGs with Spin-Orbit Coupling

Ginzburg-Landau theory of defects in d-wave superconductors.

Dynamic softening of vortex lines in YBa2Cu3O7−δ single crystals

Gate-induced enhancement of spin-orbit coupling in dilute fluorinated graphene

Charge and spin transport in nanoscopic structures with spin orbit coupling