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Kagome spin liquid

The antiferromagnetic spin-1/2 Heisenberg model on a kagome lattice is one of the most paradigmatic models of spin liquids but yet the precise nature of its ground state is still highly debated. In this talk, I will present our numerical study (DMRG simulation) and theoretical study, supporting the kagome spin liquid is a U(1) Dirac spin liquid. On the numerical side, I will discuss the spin gap of the kagome spin liquid, and more importantly the ``excitation spectrum" (from DMRG) showing sharp Dirac cones that perfectly match the U(1) Dirac spin liquid. We also discuss the scaling of entanglement entropy supporting the Dirac spin liquid.  On the theoretical side, we reveal an interesting connection between the kagome spin liquid, chiral spin liquid, symmetry protected topological phase and deconfined criticality. Specifically, we reformulate the kagome spin model ``exactly" into a lattice gauge model, in which the spin liquid phase can be studied more controllably.  We show that in such unbiased framework, the previous discovered chiral spin liquid is indeed a gauged U(1) symmetry protected topological (SPT) phase, the kagome spin liquid can be visualized as a gauged deconfined critical point (between a U(1) SPT and a superfluid).