ABSTRACT We present an extension to the 2D functional renormalization group to efficiently treat interactions on the surface or at interfaces of 3D systems. As an application, we consider a semi‐infinite stack of 2D square lattices, including a Hubbard interaction on the surface layer and an alternating interlayer coupling. We investigate how strongly correlated states of the decoupled 2D Hubbard model on the surface evolve under inclusion of such an SSH‐like interlayer coupling. For large parts of the phase diagram as a function of the interlayer hopping parameters, the physics of the 2D system prevails, with antiferromagnetic, superconducting ‐wave, and ferromagnetic correlations taking center stage. However, for intermediate interlayer couplings the superconducting state at intermediate interaction strengths separates into two regimes by a small region of incommensurate spin‐density‐wave and spin‐bond order, enabling the potential realization of chiral spin‐bond order.
We investigate the quantum phase transitions in the half-filled ionic Hubbard model on a two-dimensional (2D) square lattice using the variational cluster approach (VCA). We present explicit evidence for the tendency toward a novel intermediate phase in this model. This phase is characterized by bond-located magnetization. For weak Coulomb repulsion U , the system is a band insulator, and then undergoes a transition to the intermediate phase at the first-phase boundary U = U c1 . As U is increased beyond the second transition point U c2 , there occurs a Mott insulator accompanied by a long-range antiferromagnetic (AF) order. The bond-located spin density wave competes with the antiferromagnetism while the charge-density modulation exists all the way due to the staggered potential Δ.
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 $n<\ensuremath{\approx}0.78$ 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.