Bond excitations in the pseudogap phase of the Hubbard model

Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest-neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with U equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long-range correlations are considered. The strong correlation between excitations on parallel neighboring bonds suggests bond singlet dimerization. The suppression of divergence for n <approximate to 0.78 implies that for these model parameters, this is a quantum critical point which separates the unconventional pseudogap region characterized by bond order from a conventional Fermi liquid.