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Phases of matter are sharply defined in the thermodynamic limit. One majorchallenge of accurately simulating quantum phase diagrams of interactingquantum systems is due to the fact that numerical simulations usually deal withthe energy density, a local property of quantum wavefunctions, whileidentifying different quantum phases generally rely on long-range physics. Inthis paper we construct generic fully symmetric quantum wavefunctions undercertain assumptions using a type of tensor networks: projected entangled pairstates, and provide practical simulation algorithms based on them. We find thatquantum phases can be organized into crude classes distinguished by short-rangephysics, which is related to the fractionalization of both on-site symmetriesand space-group symmetries. Consequently, our simulation algorithms, which areuseful to study long-range physics as well, are expected to be able to sharplydetermine crude classes in interacting quantum systems efficiently. Examples ofthese crude classes are demonstrated in half-integer quantum spin systems onthe kagome lattice. Limitations and generalizations of our results arediscussed.

Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics