  We construct energy-optimized resonating valence bond wavefunctions as a
means to sketch out the zero-temperature phase diagram of the square-lattice
quantum Heisenberg model with competing nearest- (J1) and
next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an
accurate representation of the magnetically disordered intermediate phase
(centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still
controversial) but on exploring whether and how the Marshall sign structure
breaks down in the vicinity of the phase boundaries. Numerical evaluation of
two- and four-spin correlation functions is carried out stochastically using a
worm algorithm that has been modified to operate in either of two modes: one in
which the sublattice labelling is fixed beforehand and another in which the
worm manipulates the current labelling so as to sample various sign
conventions. Our results suggest that the disordered phase evolves continuously
out of the (pi,pi) Neel phase and largely inherits its Marshall sign structure;
on the other hand, the transition from the magnetically ordered (pi,0) phase is
strongly first order and involves an abrupt change in the sign structure and
spatial symmetry as the results of a level crossing.
