We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping
t and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction
U and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.
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 have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.