  Exploiting the matrix-product-state based density-matrix renormalization
group (DMRG) technique we study the one-dimensional extended ($U$-$V$) Hubbard
model with explicit bond dimerization in the half-filled band sector. In
particular we investigate the nature of the quantum phase transition, taking
place with growing ratio $V/U$ between the symmetry-protected-topological and
charge-density-wave insulating states. The (weak-coupling) critical line of
continuous Ising transitions with central charge $c=1/2$ terminates at a
tricritical point belonging to the universality class of the dilute Ising model
with $c=7/10$. We demonstrate that our DMRG data perfectly match with
(tricritical) Ising exponents, e.g., for the order parameter $\beta=1/8$ (1/24)
and correlation length $\nu=1$ (5/9). Beyond the tricritical Ising point, in
the strong-coupling regime, the quantum phase transition becomes first order.
