Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice

TL;DR

This study uses tensor network methods to analyze the ground state of the spin-1/2 Heisenberg antiferromagnet on the Shuriken lattice, revealing a valence bond crystal with specific magnetic plateaus.

Contribution

It introduces tensor network techniques to identify the valence bond crystal ground state and magnetic plateaus on the Shuriken lattice, providing the lowest energy estimates for this model.

Findings

Valence bond crystal with resonances over length six loops as ground state

Identification of 0, 1/3, and 2/3 magnetization plateaus

Lowest reported ground state energy estimate for the model

Abstract

We investigate the ground state of the spin $S=1/2$ Heisenberg anti-ferromagnet on the Shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite projected entangled pair and simplex states considering states with different sizes of the unit cells. We show that a valence bond crystal with resonances over length six loops emerges as the ground state (at any given finite bond dimension) yielding the lowest reported estimate of the ground state energy $E_0/J = -0.4410 \pm 0.0001$ for this model, estimated in the thermodynamic limit. We also study the model in the presence of an external magnetic field and find the emergence of $0$, $1/3$ and $2/3$ magnetization plateaus with states respecting translation and point group symmetries that feature loop-four plaquette resonances instead.