Plaquette Renormalization Scheme for Tensor Network States

TL;DR

This paper introduces a variational plaquette renormalization scheme for contracting 2D tensor networks, improving the accuracy of quantum state approximations, demonstrated on the transverse-field Ising model.

Contribution

It proposes a novel tensor renormalization method using auxiliary tensors for efficient 2D tensor network contraction, enhancing variational energy minimization.

Findings

Small tensors yield significantly better results than mean-field approximations.

The scheme accurately captures the quantum phase transition.

Test results show improved performance with minimal tensor sizes.

Abstract

We present a method for contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations (renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index tensors. The scheme is variational, and thus the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state.