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We investigate the role of a scalar tetraquark state for the description ofnuclear matter within the parity doublet model in the mirror assignment. In thedilatation-invariant version of the model a nucleon-nucleon interaction termmediated by the lightest scalar tetraquark field naturally emerges. At nonzerodensity one has, beyond the usual chiral condensate, also a tetraquarkcondensate. The behavior of both condensates and the restoration of chiralsymmetry at high density are studied. It is shown that this additional scalardegree of freedom affects non negligibly the properties of the medium.

Nuclear matter within a dilatation-invariant parity doublet model: the role of the tetraquark at nonzero density