Fig. 6: The dimerized structure at half filling.
a A sketch of bond disproportionated lattice structure. The red and blue dots indicate the s and px,y orbitals, respectively, while the black arrow indicate the displacement pattern of each oxygen atom in the bond disproportionated structure. Panels b and c plot the lattice displacement correlation functions \(\langle {\hat{X}}_{{\bf{r}},x}{\hat{X}}_{0,x}\rangle\) and \(\langle {\hat{X}}_{{\bf{r}},y}{\hat{X}}_{0,y}\rangle\) as a function of distance r = nxa + nyb, respectively. Here, a = (a, 0) and b = (0, a) are the primitive vectors along x- and y-directions, respectively. Panel d plots the real-space displacement correlation function \(\langle {\hat{X}}_{{\bf{r}},y}{\hat{X}}_{0,x}\rangle\) indicating the two-sublattice structure of the bond disproportionated state. The distance between two nearest Bi atom in the undistorted square structure is a. The inverse temperature is \({(\beta {t}_{sp})}^{-1}=0.1\). The error bars represent 1σ statistical errors, which were obtained from the sample variances measured during Monte Carlo sampling.
