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arXiv · 2211.16932

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

Philipp Schmoll·Augustine Kshetrimayum·Jan Naumann·Jens Eisert·Yasir Iqbal
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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.

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Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal. 2022-11-30. Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice. https://doi.org/10.1103/physrevb.107.064406

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