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.

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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 present some numerical results to show that in a simple model which includes Cu3d and O 2p orbitals together with inter and intra atomic correlations pairing between holes can occur due to charge transfer excitations. We present also a simple approximation to derive an effective Hamiltonian containing an interaction between particles which is attractive for some values of the different microscopic parameters.

Superconductivity and charge transfer excitations in high T c superconductors

Persistent currents in a superconducting ring with a normal and spin-flip junction

We use a variational procedure to show, starting with the flux-phase state of a Heisenberg model, that holes added to the system behave as anyons. The hole distorts the gauge flux in its surroundings. The amount of flux carried by the hole depends on the ratio between the magnetic- ({ital J}) and the kinetic- ({ital t}) energy parameters. For {ital J}/{ital t}{r arrow}0 the quasiparticles are fermions, while for {ital J}/{ital t}{r arrow}{infinity} they are semions.

Anyons in spin liquids

Using numerical exact diagonalization techniques we study the zero-temperature properties of a substitutional magnetic impurity in a one-dimensional correlated system described by the repulsive Hubbard model. We calculate the static spin and charge correlation functions and find that, while the spin correlation maintains a 2 k F periodicity when increasing the Hubbard U , the charge correlations show Friedel oscillations with a 4 k F periodicity for large values of U . We also present results for the static susceptibility at the impurity site. This susceptibility shows a non-monotonic behaviour as a function of U for the doped case. For small values of U the Kondo singlet seems to be more strongly bounded than in the non-interacting ( U = 0) case.

Finite-size study of a magnetic impurity in a strongly correlated electronic system

We calculate the one-hole spectral function for the polarized t — J model using exact diagonalization for a finite size cluster. A well-defined quasiparticle peak appears at the bottom of the spectrum for intermediate values of J . The momentum of the quasiparticle corresponding to the bottom of the band varies with the magnetization and the strength of the coupling J . We use these results to analyze the one-particle spectra in strong coupling superconductors.

C. A. Balseiro

Papers

Superconductivity and charge transfer excitations in high T c superconductors

Persistent currents in a superconducting ring with a normal and spin-flip junction

Anyons in spin liquids

Finite-size study of a magnetic impurity in a strongly correlated electronic system

Dynamics of one hole in the polarized t−J model