Renormalization groups and variational states in an interacting 1D quantum model

Tomotoshi Nishino, Kouichi Okunishi

The authors 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 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.

Michael N. Barber

A. Langari, Vahid Karimipour

Luis J. Boya, Alejandro Rivero

We build a toy model of the Wilson-Kogut renormalization group in one dimensional Quantum Mechanics. With it, we show how the RG flow in the space of 1-D S matrices of finite range defines, as renormalized interactions, the known four parametric set of contact interactions, thus providing a suitable framework for its study.

Tomotoshi Nishino, Yasuhiro Hieida, Kouichi Okunishi +2 more

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. Variational states represented as products of local tensols have been used widely for calculating the ground-state energy in one-dimensional (1D) quantum systems and the free energy in two-dimensional (2D) classical statistical systems. In 1941 Kramers and Wannier calculated a lower bound of the partition function of the 2D

L. S. Campana, Alvaro Caramico D’Auria, Francesco Esposito +1 more