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Exploiting the matrix-product-state based density-matrix renormalizationgroup (DMRG) technique we study the one-dimensional extended ($U$-$V$) Hubbardmodel with explicit bond dimerization in the half-filled band sector. Inparticular we investigate the nature of the quantum phase transition, takingplace with growing ratio $V/U$ between the symmetry-protected-topological andcharge-density-wave insulating states. The (weak-coupling) critical line ofcontinuous Ising transitions with central charge $c=1/2$ terminates at atricritical point belonging to the universality class of the dilute Ising modelwith $c=7/10$. 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, inthe strong-coupling regime, the quantum phase transition becomes first order.

Critical behavior of the extended Hubbard model with bond dimerization