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We discuss quantum many-body systems with lattice translation and discreteonsite symmetries. We point out that, under a boundary condition twisted by asymmetry operation, there is an exact degeneracy of ground states if the unitcell forms a projective representation of the onsite discrete symmetry. Basedon the quantum transfer matrix formalism, we show that, if the system isgapped, the ground-state degeneracy under the twisted boundary condition alsoimplies a ground-state (quasi-)degeneracy under the periodic boundaryconditions. This gives a compelling evidence for the recently proposedLieb-Schultz-Mattis type ingappability due to the onsite discrete symmetry intwo and higher dimensions.

Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries