Tomotoshi Nishino

Corner Transfer Matrix Renormalization Group Method

We propose a new fast numerical renormalization group method – the corner transfer matrix renormalization group (CTMRG) method – which is based on a unified scheme involving Baxters corner transfer matrix method and Whites density matrix renormalization group method. The key point is that a product of four corner transfer matrices coincides with the density matrix. We formulate CTMRG as a renormalization group for 2D classical models.

EQUIVALENCE OF THE VARIATIONAL MATRIX PRODUCT METHOD AND THE DENSITY MATRIX RENORMALIZATION GROUP APPLIED TO SPIN CHAINS

We study the relationship between the Density Matrix Renormalization Group (DMRG) and the variational matrix product method (MPM). In the latter method one can also define a density matrix whose eigenvalues turn out to be numerically close to those of the DMRG. We illustrate our ideas with the spin-1 Heisenberg chain, where we compute the ground-state energy and the spin correlation length. We also give a rotational invariant formulation of the MPM.

Product Wave Function Renormalization Group.

We propose a fast numerical renormalization group method-the product wave function renormalization group (PWFRG) method-for 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed as a matrix product, is improved through a self-consistent calculation. The new method has the same fixed point as the density matrix renormalization group method.

Corner transfer matrix algorithm for classical renormalization group

We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxters corner transfer matrix (CTM), for two-dimensional ( d = 2) classical lattice models. The new method performs the renormalization group transformation according to Whites density matrix algorithm, so that variational free energies are minimized within a restricted degree of freedom. As a consequence of the renormalization, spin variables on each corner of CTM are replaced by a m -state block spin variable. It is shown that the thermodynamic functions and critical exponents of the q = 2, 3 Potts models can be precisely evaluated by use of the renormalization group method.

Two-Dimensional Tensor Product Variational Formulation

We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model.

Analysis of derivative spectrum of indirect exciton absorption in silicon

Abstract It is shown that an analysis of the wavelength modulated absorption spectrum enables us to estimate the transition matrix elements in indirect absorption. The transition matrix elements in silicon are determined to be 0.110 h A for indirect absorption with the TO phonon, 0.0367 h A for the LO phonon and 0.0178 h A for the TA phonon.

Direct observation of split-off exciton and phonon structures in absorption spectrum of silicon

Abstract The split-off band exciton of silicon has been observed in the absorption spectrum by using a wavelength modulation technique. The spin-orbit splitting of the valence band is determined to be 44.1 ± 0.3 meV at 1.8 °K. The structures associated with some two-phonon indirect transitions have also been observed in the absorption spectrum.

Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons.

The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant

Fixed Point of the Finite System DMRG

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Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

and the Coulomb interaction