Kagome model for a ${\mathbb{Z}}_2$ quantum spin liquid

Abstract

We present a study of a simple model antiferromagnet consisting of a sum of nearest neighbor SO($N$) singlet projectors on the Kagome lattice. Our model shares some features with the popular $S=1/2$ Kagome antiferromagnet but is specifically designed to be free of the sign-problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb{Z}}_2$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.

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• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Stochastic Series Expansion Methods
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
• Classical and quantum spin liquids
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Topological characterization of magnon-polaron bands and thermal Hall conductivity in a frustrated kagome antiferromagnet
• Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach