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