| Anderson's idea of a (short-ranged) resonating valence bond spin liquid has been the first ever proposal of what we now call a topologically ordered phase. Since then, a wealth of exactly solvable lattice models has been constructed that have topologically ordered ground states. For a long time, however, it has been difficult to realize Anderson's original vision in this way, according to which the ground state has an unbroken SU(2) spin rotational symmetry, and is dominated by fluctuation of singlet bonds. The kagome lattice is the simplest lattice geometry for which a parent Hamiltonian stabilizing a prototypical spin-1/2 short-ranged RVB wave function has been constructed and strong evidence has been given that this state belongs to a topological phase. This talk will review the construction of RVB parent Hamiltonians for the kagome, the discussion of their ground state uniqueness modulo topological degeneracies, and the numerical evaluation of correlation functions, for which the traditional Sutherland loop-gas approach suffers from a sign problem. |
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