Fig. 7: Dimer correlator.

The correlator \(g(r)=\langle {b}_{L/2}^{{{\dagger}} }{b}_{L/2+r}\rangle\), with b_i corresponding to the annihilator for a dimer, is shown in the opposite regimes of small (0.1) and large (10.0) values of \(\frac{h}{t}\), at the filling \(\nu =\frac{2}{3}\) and at the magnetic coupling J/t = 1.8. To minimize boundary-effects, we evaluate the correlator starting from the middle point of the chain. Notice that, since the model (2) is defined on a chain of length L = 120, dimer operators will be defined on a chain of length L − 1 = 119 and r will be allowed to vary up to 59. The main plot in log-log scale makes it evident that the algebraic decays in the two regimes are almost superimposed and confirms that the effective description provided by Eq. (6) for ℓ_AB = 2 is valid in both cases. In the inset, the same plot is in linear scale up to r = 30 for a better visualization. The data points are fitted to g(r) = α r^−β. For h/t = 0.1(10.0), we find α ~ 0.154(0.154) and β ≈ 1.920(1.925).