Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid, a bosonic analogue of the fractional quantum Hall effect, put forward by Kalmeyer and Laughlin in 1987. Elusive for many years, recent times have finally seen this phase realized in various models, which, however, remain somewhat artificial. Here we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We discuss the emergent phase from a network model perspective and present an unambiguous numerical identification and characterization of its universal topological properties, including groundstate degeneracy, edge physics and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.
The theoretical description of non-Fermi liquids is among the most challenging questions in strongly correlated quantum matter. While there are many experimental candidates for such phases, few examples can be studied using controlled theoretical approaches. Here we introduce a novel conceptual perspective to analytically describe the non-Fermi liquid physics of gapless spin liquids arising in a family of two-and three-dimensional Kagome models. We first discuss a symmetry-protection mechanism that is responsible for the stability of the gapless phase. We then re-cast the two-dimensional Kagome spin model as a chiral Kondo lattice model that can be tackled analytically using what is in a sense a generalization of coupled-wire constructions. We provide extensive numerical evidence for a gapless spin liquid in the two-dimensional Kagome model and discuss generalizations to three dimensions. 2
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