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We explore a possible phase where chiral $SU(2)_L \times SU(2)_R$ symmetry isspontaneously broken while its center $Z_2$ symmetry remains unbroken and itsconsequence on thermal quantities. In this phase, chiral symmetry breaking isdriven by a quartic quark condensate although a bilinear quark condensatevanishes. A Ginzburg-Landau free energy leads to a new tricritical point (TCP)between the $Z_2$ broken and unbroken phases. Furthermore, a critical point canappear even in the chiral limit where explicit breaking is turned off, insteadof a TCP at which restoration of chiral and its center symmetries takes placesimultaneously. The net quark number density exhibits an abrupt change near therestoration of the center symmetry rather than that of the chiral symmetry.Hadron masses in possible phases are also studied in a linear sigma model. Weshow that, in the $Z_2$ symmetric phase, the $\bar{q}q$-type scalar meson withzero isospin I=0 splits from the $\bar{q}q$-type pseudoscalar meson with I=1.

Enhancement of quark number susceptibility with an alternative pattern of chiral symmetry breaking in dense matter