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

SynopsisThe density matrix renormalization group (DMRG) method is applied to the interaction round a face (IRF) model. When the transfer matrix is asymmetric, singular-value decomposition of the density matrix is required.A trial numerical calculation is performed on the square lattice Ising model, which is a special case of the IRF model.

We present a rotationally invariant matrix product method (MPM) of isotropic spin chains. This allows us to deal with a larger number of variational MPM parameters than those considered earlier by other authors. We also show the relation between the MPM and the DMRG method of White. In our approach the eigenstates of the density matrix associated with the MPM are used as variational parameters together with the standard MPM parameters. We compute the ground state energy density and the spin correlation length of the spin 1 Heisenberg chain.

We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group transformation according to White's density matrix algorithm, so that variational free energies are minimized within a restricted degree of freedom m. 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.Comment: 20 pages, 10 ps figures, JPSJ style files are include

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.Comment: 9 pages, 4 figures, submitted to Prog. Theor. Phy

( ) SynopsisThe authors propose a fast numerical renormalization group method -the product wave function renormalization group (PWFRG) methodfor 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed by 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.-to appear in J. Phys. Soc. Jpn. -1

We apply a recently developed numerical renormalization group, the cornertransfer-matrix renormalization group (CTMRG), to 2D classical lattice models at their critical temperatures. It is shown that the combination of CTMRG and the finite-size scaling analysis gives two independent critical exponents.

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is investigated through trial applications to the 3D Ising model and the 3D 3-state Potts model.