Renormalization Group Transformation for the Wave Function

Hiroshi Ueda, Tomotoshi Nishino, Koichi Kusakabe

We report a way of wave function estimation for the density matrix renormalization group (DMRG) method applied to quantum systems, which has 2-site modulation, when the system size extension is necessary in both the finite and the infinite algorithms. The estimation is performed by renormalization group (RG) transformation applied to the ground state wave function, which is represented as the matrix product. This RG scheme is known as the product wave function renormalization group (PWFRG) method. In order to treat the 2-site modulation, the operation of the RG transformation is shifted by amount of 2 lattice sites. It turns out that this 2-site shift algorithm provides better wave function estimation in the thermodynamic limit, compared with the previously known PWFRG algorithm.

Robert König, Ben W. Reichardt, Guifré Vidal

We construct an explicit renormalization-group transformation for Levin and Wen's string-net models on a hexagonal lattice. The transformation leaves invariant the ground-state ``fixed-point'' wave function of the string-net condensed phase. Our construction also produces an exact representation of the wave function in terms of the multiscale entanglement renormalization ansatz (MERA). This sets the stage for efficient numerical simulations of string-net models using MERA algorithms. It also provides an explicit quantum circuit to prepare the string-net ground-state wave function using a quantum computer.

U. Köbler, A. Hoser

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.

John C. Collins