Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice

TL;DR

This paper applies the vertical density matrix algorithm (VDMA), a tensor network method, to study the ground state properties of the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice, exploring phases and accuracy.

Contribution

The study adapts the VDMA for the XXZ model on the checkerboard lattice and evaluates its accuracy in determining ground state energies and phases.

Findings

VDMA provides reliable ground state energy estimates.

Weak frustration corresponds to Néel order.

Strong frustration phase remains unclear.

Abstract

Vertical density matrix algorithm (VDMA), a tensor product state formulation of the ``higher-dimensional'' density matrix renormalization group, is applied to the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice. The VDMA was, in the preceding study, applied to the transverse field Ising model on the square lattice and the three-dimensional classical Ising model. In the present paper, its implementation procedure is modified in order to apply the VDMA to the XXZ model. Numerical accuracy of the VDMA is investigated for the XXZ model on the square lattice, which shows that the method gives reliable results for the ground state energy. In the frustrated region, VDMA results are compared with a simple calculation based on a magnetically disordered state. It is found that the weakly frustrated region is in the N\'{e}el ordered phase, while in the strongly frustrated region the realized phase cannot be identified clearly by the obtained results.