  We study the two-dimensional $t$-$J$ model on a square lattice using infinite
projected entangled pair states (iPEPS). At small doping, multiple orders, such
as antiferromagnetic order, stripe order and superconducting order, are
intertwined or compete with each other. We demonstrate the role of spin
symmetry at small doping by either imposing SU(2) spin symmetry or its U(1)
subgroup in the iPEPS ansatz, thereby excluding or allowing spontaneous
spin-symmetry breaking respectively in the thermodynamic limit. From a detailed
comparison of our simulations, we provide evidence that stripe order is pinned
by long-range antiferromagnetic order. We also find that SU(2) iPEPS, which
enforces a spin-singlet state, yields a uniform charge distribution and favors
d-wave singlet pairing.
