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

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.

9 pages, 11 figures, 2 tables, some references added

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• $\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Tensor network analysis of the maple-leaf antiferromagnet spangolite
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Variational optimization of projected entangled-pair states on the triangular lattice
• The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
• Magnetic phases of the periodic Anderson model in two dimensions
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study