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

TL;DR

This paper constructs and analyzes a topological $ m{Z}_2$ RVB quantum spin liquid state on the ruby lattice using PEPS, confirming its topological nature through entanglement entropy and exploring its relation to a quantum-dimer model.

Contribution

It introduces a PEPS-based RVB state on the ruby lattice with topological properties and connects it to a potential parent quantum-dimer Hamiltonian.

Findings

Identifies four topological sectors in the RVB state.

Confirms topological order via entanglement entropy with $ egative m{ln} 2$.

Provides ground-state energy comparison with Heisenberg model.

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, $\gamma=-\rm{ln}\ 2$, 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.