  We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of
quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times
\mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with
two flavors of quarks without an anomaly. The model also contains a coupling
that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD
anomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$
the model contains massless pions and massive bosonic baryons similar to QCD
with an even number of colors. In this work we study the $T-\mu_B$ phase
diagram of the model and show that it contains three phases : (1) A chirally
broken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluid
phase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. We
find that the nature of the finite temperature chiral phase transition and in
particular the location of the tricritical point that seperates the first order
line from the second order line is affected significantly by the anomaly.
