  We investigate the spin-1/2 Heisenberg model on a rectangular lattice, using
the Gutzwiller projected variational wave function known as the staggered flux
state. Using Monte Carlo techniques, the variational parameters and static
spin-structure factor for different coupling anisotropies $\gamma=J_y/J_x$ are
calculated. We observe a gradual evolution of the ground state energy towards a
value which is very close to the 1D estimate provided by the Bethe ansatz and a
good agreement between the finite size scaling of the energies. The spin-spin
correlation functions exhibit a power-law decay with varying exponents for
different anisotropies. Though the lack of N\'eel order makes the staggered
flux state energetically unfavorable in the symmetric case $\gamma=1$, it
appears to capture the essence of the system close to 1D. Hence we believe that
the staggered flux state provides an interesting starting point to explore the
crossover from quantum disordered chains to the N\'eel ordered 2D square
lattices.
