  The property of quantum many-body systems under spatial reflection and the
relevant physics of renormalization group (RG) procedure are revealed. By
virtue of the matrix product state (MPS) representation, various attributes for
translational invariant systems associated with spatial reflection are
manifested. We demonstrate subsequently a conservation rule of the conjugative
relation for reflectional MPS pairs under RG transformations and illustrate
further the property of the fixed points of RG flows. Finally, we show that a
similar rule exists with respect to the target states in the density matrix
renormalization group algorithm.
