  Aiming to describe frustrated quantum magnets with non-magnetic singlet
ground states, we have extended the Rokhsar-Kivelson (RK) loop-expansion to
derive a generalized Quantum Dimer Model containing only connected terms up to
arbitrary order. For the square lattice frustrated Heisenberg antiferromagnet
(J1-J2-J3 model), an expansion up to 8th order shows that the leading
correction to the original RK model comes from dimer moves on length-6 loops.
This model free of the original sign problem is treated by advanced numerical
techniques. The results suggest that a rotationally anisotropic plaquette phase
is the ground state of the Heisenberg model in the parameter region of maximum
frustration.
