Kagome model for a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> quantum spin liquid
Matthew S. Block, Jonathan D’Emidio, Ribhu K. Kaul
Abstract
We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor $\mathrm{SO}(N)$ 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.