  For strongly correlated electrons the relation between total number of charge
carriers $n_e$ and the chemical potential $\mu$ reveals for large Coulomb
energy the apparently paradoxical pinning of $\mu$ within the Mott gap, as
observed in high-$T_c$ cuprates. By unravelling consequences of the non-trivial
topology of the charge gauge U(1) group and the associated ground state
degeneracy we found a close kinship between the pinning of $\mu$ and the
zero-temperature divergence of the charge compressibility $\kappa\sim\partial
n_e/\partial\mu$, which marks a novel quantum criticality governed by
topological charges rather than Landau principle of the symmetry breaking.
