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 calculate exactly the one-particle spectral densities and Hall conductivity for the two-dimensional Hubbard model in the large-U limit, for two different finite clusters. The Fermi surface obtained from the one-particle spectral functions is consistent with Luttinger's theorem, but the Hall conductivity changes from electronlike for a dilute system to holelike for a nearly half-filled system, indicating the deconfinement of charge and spin excitations in a two-dimensional system.

Hall conductivity and Fermi surface in highly correlated systems.

In this paper a theory of superconductivity for metals in which there are localized spins is presented. The spins interact with the conduction electrons via an exchange interaction and with one another via a direct Heisenberg interaction, as well as indirectly via the conduction electrons. The spins are treated as classical vectors in a mean-field approximation. The superconducting pair-breaking mechanism is treated in the approximation of Abrikosov and Gor'kov. Complete interplay of magnetization and pair-breaking processes is taken into account. Phase diagrams are presented. A treatment of alloys of two different magnetic ions is included in a simple approximation. All results are in good qualitative agreement with the experiment.

Superconductivity and ferromagnetism

We investigate the coherent mixing of co-propagating edge channels in a quantum Hall bar produced by step potentials In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step Charge density probability has been also calculated even for the case where the step is smoothened

https://fisica.cab.cnea.gov.ar/solidos/personales/usaj/mypdf/Venturelli2011%20-%20Edge%20channel%20mixing%20induced%20by%20potential%20steps%20in%20an%20integer%20quantum%20Hall%20system.pdf

Edge channel mixing induced by potential steps in an integer quantum Hall system

We describe a device where the nonlocal spin-spin interaction between quantum dots (QDs) can be turned on and off with a small magnetic field. The setup consists of two QDs at the edge of two two-dimensional electron gases (2DEGs). The QDs' spins are coupled through a RKKY-like interaction mediated by the electrons in the 2DEGs. A magnetic field B(z) perpendicular to the plane of the 2DEG is used as a tuning parameter. When the cyclotron radius is commensurate with the interdot distance, the spin-spin interaction is amplified by a few orders of magnitude. The sign of the interaction is controlled by finely tuning B(z). Our setup allows for several dots to be coupled in a linear arrangement and it is not restricted to nearest-neighbor interaction.

https://fisica.cab.cnea.gov.ar/solidos/personales/usaj/mypdf/Usaj2005a%20-%20Tuning%20the%20Nonlocal%20Spin-Spin%20Interaction%20between%20Quantum%20Dots%20with%20a%20Magnetic%20Field.pdf

Tuning the nonlocal spin-spin interaction between quantum dots with a magnetic field.

We present long-term relaxation measurements of the irreversible magnetization in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystals with columnar defects Within the single vortex pinning regime we find a nonglassy response at intermediate currents, in between the half loops and superkinks glassy regimes We demonstrate that such behavior is due to double kink excitations whose critical nucleus has a size independent of current, and occur even in the presence of pinning energy dispersion

C. A. Balseiro

Papers

Hall conductivity and Fermi surface in highly correlated systems.

Superconductivity and ferromagnetism

Edge channel mixing induced by potential steps in an integer quantum Hall system

Tuning the nonlocal spin-spin interaction between quantum dots with a magnetic field.

Nonglassy relaxation by double kinks in YBa 2 Cu 3 O 7-δ with columnar defects