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K Okunishi

Publications and source records attributed to K Okunishi.

3 recordsLinked to original sources
PubMed2001

Vertical density matrix algorithm: a higher-dimensional numerical renormalization scheme based on the tensor product state ansatz.

We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation, we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.

Journal Article↗
PubMed1999

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.

Journal Article↗