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The virial theorem for a system of interacting electrons in a crystal, whichis described within the framework of the tight-binding model, is derived. Weshow that, in particular case of interacting massless electrons in graphene andother Dirac materials, the conventional virial theorem is violated. Startingfrom the tight-binding model, we derive the generalized virial theorem forDirac electron systems, which contains an additional term associated with amomentum cutoff at the bottom of the energy band. Additionally, we derive thegeneralized virial theorem within the Dirac model using the minimization of thevariational energy. The obtained theorem is illustrated by many-bodycalculations of the ground state energy of an electron gas in graphene carriedout in Hartree-Fock and self-consistent random-phase approximations.Experimental verification of the theorem in the case of graphene is discussed.

Generalized virial theorem for massless electrons in graphene and other Dirac materials