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arXiv · 1912.06215

Topological $\mathbb{Z}_2$ RVB quantum spin liquid on the ruby lattice

Saeed S. Jahromi·Roman Orus
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Abstract

We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension $D=3$. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, $γ=-\rm{ln}\ 2$, consistent with that of a $\mathbb{Z}_2$ topological quantum spin liquid. We also calculate the ground-state energy of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

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Saeed S. Jahromi, Roman Orus. 2019-12-12. Topological $\mathbb{Z}_2$ RVB quantum spin liquid on the ruby lattice. https://doi.org/10.1103/physrevb.101.115114

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