Tensor network study of the spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> Heisenberg antiferromagnet on the shuriken lattice
Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal
Abstract
We investigate the ground state of the spin $S=\frac{1}{2}$ Heisenberg antiferromagnet 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 ${E}_{0}/J=\ensuremath{-}0.4410\ifmmode\pm\else\textpm\fi{}0.0001$ 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, $\frac{1}{3}$, and $\frac{2}{3}$ magnetization plateaus. The $\frac{1}{3}$ and $\frac{2}{3}$ plateau states respect translation and point group symmetries and feature loop-four plaquette resonances.