Numerical Renormalization Approach to Two-Dimensional Quantum Antiferromagnets with Valence-Bond-Solid Type Ground State

TL;DR

This paper introduces a numerical renormalization approach to analyze the ground-state properties of two-dimensional quantum antiferromagnets with valence-bond-solid states, using tensor product states and transfer-matrix methods.

Contribution

It develops a novel numerical method combining tensor networks and transfer-matrix techniques to study 2D quantum spin systems with VBS ground states.

Findings

Accurate calculation of correlation length and sublattice magnetization.

Correlation length behavior similar in 2D honeycomb and 1D chain models.

Method effectively handles anisotropic deformations in VBS models.

Abstract

We study the ground-state properties of the two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The ``product-of-tensors'' form of the ground-state wavefunction of the system is utilized to associate it with an equivalent classical lattice statistical model which can be treated by the transfer-matrix method. For diagonalization of the transfer matrix, we employ the product-wavefunction renormalization group method which is a variant of the density-matrix renormalization group method. We obtain the correlation length and the sublattice magnetization accurately. For the anisotropically ``deformed'' S=3/2 VBS model on the honeycomb lattice, we find that the correlation length as a function of the deformation parameter behaves very much alike as that in the S=3/2 VBS chain.