Kouichi Okunishi

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.

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.

MIDDLE-FIELD CUSP SINGULARITIES IN THE MAGNETIZATION PROCESS OF ONE-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.

Magnetization process of a one-dimensional quantum antiferromagnet: The product-wave-function renormalization group approach☆

Abstract The product-wave-function renormalization group method, a new numerical renormalization group scheme proposed recently, is applied to one-dimensional quantum spin chains in a magnetic field. We find the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.

Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit.

We study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix (M(CTM)) and the density matrix (M(DM)) in the density-matrix renormalization group. We utilize the relationship M(DM)=M(4)(CTM), which holds for noncritical systems in the thermodynamic limit. We derive the exact and universal asymptotic form of the M(DM) eigenvalue distribution for a class of integrable models in the massive regime. For nonintegrable models, the universal asymptotic form is also verified by numerical renormalization group calculations.

Novel ordering of an S = 1/2 quasi-1d Ising-like antiferromagnet in magnetic field.

High-field specific heat measurements on BaCo(2)V(2)O(8), which is a good realization of an S=1/2 quasi-one-dimensional (1D) Ising-like antifferomagnet, have been performed in magnetic fields up to 12 T along the chain and at temperature down to 200 mK. We have found a new magnetic ordered state in the field-induced phase above H(c) approximately 3.9 T. We suggest that a novel type of the incommensurate order, which is caused by the quantum effect inherent in the S=1/2 quasi-1D Ising-like antiferromagnet, appears in the field-induced phase.

Antiferromagnetic zigzag spin chain in magnetic fields at finite temperatures

We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization-group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process

Quantum spin nanotubes?frustration, competing orders and criticalities

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