Critical behavior of the extended Hubbard model with bond dimerization

Abstract

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 β=1/8 (1/24) and correlation length ν=1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.