In this talk, I will discuss the progress/success of
Z2 RVB spin liquid phase on the kagome lattice.
For the kagome lattice there exists a parent Hamiltonian
for this state, but even in the absence of a known Hamiltonian, wave functions
of RVB type are interesting as such. I will briefly discuss this Hamiltonian.
Subsequently, I will introduce a Monte Carlo (MC) scheme
to investigate the nearest neighbor version of Anderson's RVB spin-1/2 wave
function on the kagome and on the triangular lattice.
The corresponding RVB wave function on the square lattice
has recently enjoyed much attention, and it was shown that earlier findings
about the criticality of the dimer liquid wave function on the square lattice
qualitatively carry over to the analogous spin liquid wave function on this
On bipartite lattices, the spin-1/2 RVB wave functions
are amenable to MC methods based on a loop gas picture. For other lattices,
this method has a sign problem. We present a method that is free of this sign
problem, making use of a Pfaffian presentation of the wave function in the orthogonal
Ising basis. Our results for both open and periodic boundary conditions show
that spin-spin and ``singlet-singlet'' type correlation function are
Time permitting, I will also comment on further issues
stemming from the challenge of proving the existence of a spin liquid phase on
the kagome lattice.