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We study the two-dimensional $t$-$J$ model on a square lattice using infiniteprojected entangled pair states (iPEPS). At small doping, multiple orders, suchas antiferromagnetic order, stripe order and superconducting order, areintertwined or compete with each other. We demonstrate the role of spinsymmetry at small doping by either imposing SU(2) spin symmetry or its U(1)subgroup in the iPEPS ansatz, thereby excluding or allowing spontaneousspin-symmetry breaking respectively in the thermodynamic limit. From a detailedcomparison of our simulations, we provide evidence that stripe order is pinnedby long-range antiferromagnetic order. We also find that SU(2) iPEPS, whichenforces a spin-singlet state, yields a uniform charge distribution and favorsd-wave singlet pairing.

iPEPS study of spin symmetry in the doped $t$-$J$ model