Abstract:
We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the $S=1/2$ zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.

Abstract:
We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized Hamiltonian should satisfy in the thermodynamic limit is also derived from the fixed point of the recursion relation for the corner Hamiltonian. We demonstrate the renormalization group algorithm for the $S=1/2$ XXZ spin chain and show that the results are consistent with the exact solution. We further examine the renormalization group for the S=1 Heisenberg spin chain and then discuss the nature of the eigenvalue spectrum of the corner Hamiltonian for the non-integrable model.

Abstract:
We present a novel real-space renormalization group(RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cut-off parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.

Abstract:
We investigate filling dependence of the zigzag Hubbard ladder, using density matrix renormalization group method. We illustrate the chemical-potential vs. electron-density and spin gap vs. electron density curves, which reflect characteristic properties of the electron state.On the basis of the obtained phase diagram, we discuss the connection to a novel quasi-one-dimensional superconductor Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$.

Abstract:
We discuss topological disentangler for S=1 quantum spin chains in the Haldane phase. We first point out that Kennedy-Tasaki's(KT) nonlocal unitary transformation is the perfect disentangler for Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the double-fold degeneracy in the entanglement spectrum of the S=1 Heisenberg chain.

Abstract:
We discuss the relation between the Wilson's numerical renormalization group(NRG) for the Kondo impurity problem and a field theory in the background AdS_3 space time, where the radial coordinate plays a role of the controlling parameter of the effective mass scale. We find that the Wilson NRG can be described by the boundary Rindler field and then the cutoff parameter \lambda of the Wilson NRG is related to the AdS radius L through \lambda = 2k_F/\omega L, where k_F is the effective Fermi wave number. It is also found that the Rindler space is discretized with the lattice space of a=\pi/k_F.

Abstract:
To address various fisheries science problems around Japan, the Japan Fisheries Research and Education Agency (FRA) has developed an ocean forecast system by combining an ocean circulation model based on the Regional Ocean Modeling System (ROMS) with three-dimensional variational analysis schemes. This system, which is called FRA-ROMS, is a basic and essential tool for the systematic conduct of fisheries science. The main aim of FRA-ROMS is to realistically simulate mesoscale variations over the Kuroshio-Oyashio region. Here, in situ oceanographic and satellite data were assimilated into FRA-ROMS using a weekly time window. We first examined the reproducibility through comparison with several oceanographic datasets with an Eulerian reference frame. FRA-ROMS was able to reproduce representative features of mesoscale variations such as the position of the Kuroshio path, variability of the Kuroshio Extension, and southward intrusions of the Oyashio. Second, using a Lagrangian reference frame, we estimated position errors between ocean drifters and particles passively transported by simulated currents, because particle tracking is an essential technique used in applications of reanalysis products to fisheries science. Finally, we summarize recent and ongoing fisheries studies that use FRA-ROMS and mention several new developments and enhancements that will be implemented in the near future.

Abstract:
We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are briefly discussed.

Abstract:
We generalize the corner transfer matrix renormalization group, which consists of White's density matrix algorithm and Baxter's method of the corner transfer matrix, to three dimensional (3D) classical models. The renormalization group transformation is obtained through the diagonalization of density matrices for a cubic cluster. A trial application for 3D Ising model with m=2 is shown as the simplest case.

Abstract:
We investigate phase transitions of the quasi-one-dimensional XXZ model in a magnetic field, using the bosonization combined with the mean field treatment of the inter-chain interaction. We then find that the field induced incommensurate order is certainly realized in the low field region, while the transverse staggered order appears in the high field region. On the basis of the result, we discuss the field-induced phase transition recently observed for BaCo2V2O8.