Tau functions of modified CKP hierarchy

Modified CKP (mCKP) hierarchy is an important integrable hierarchy, that is related to CKP hierarchy through Miura link. It has been proven that there exists a tau pair (τ0,τ1) for mCKP hierarchy. Further we find that mCKP hierarchy can be fully determined by CKP tau function and corresponding CKP eigenfunction. Based on this, we construct mCKP tau functions by CKP Darboux transformations and also present the vacuum expectation value of free bosons. As a byproduct, determinant formula for 〈1|eH(to)β0eβn22eβn−122⋯eβ122g|0〉 is also derived.