Z2 topological orders in kagome dipolar systems: Feedback from Rydberg quantum simulator

The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological orders among the ultracold Rydberg atom arrays, we consider the possibility of searching for topological orders among the dipolar quantum magnets and polar molecules with a kagome lattice geometry. Together with other quantum interactions such as the transverse field, the dipolar interaction endows the kagome system with a similar structure as the Balents-Fisher-Girvin model and thus fosters the emergence of the \mathbb{Z}_2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:math> topological orders. We construct a \mathbb{Z}_2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:math> lattice gauge theory to access the topological ordered phase and describe the spinon and vison excitations for the \mathbb{Z}_2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:math> topological orders. We explain the spectroscopic consequences for various quantum phases as well as the experimental detection. We further discuss the rare-earth kagome magnets, ultracold polar molecules, and cluster Mott insulators for the physical realization.