We introduce a family of lattices for which the Hubbard model and its natural extensions can be quasiexactly solved, i.e., solved for the ground and low energy states. In particular, we show rigorously that the ground state of the Hubbard model with off-site Coulomb repulsions on a decorated Kagomè lattice is an ordered array of local currents. The low energy theory describing this chiral state...

We show that the quantum order parameters (QOP) associated with the transitions between a normal conductor and a superconductor in the BCS and η-pairing models and between a Mott-insulator and a superfluid in the Bose-Hubbard model are directly related to the amount of entanglement existent in the ground state of each system. This connection gives a physical meaningful interpretation to these Q...

In this paper we study the relation between long cycles and Bose-Condensation in the Infinite range Bose-Hubbard Model with a hard core interaction. We calculate the density of particles on long cycles in the thermodynamic limit and find that the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation but this density is not equal to that of the Bo...

We construct XX-and Hubbard-like models based on unitary superalgebras gl(N |M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N |M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang–Baxter equation, we derive the corresponding local Hamilt...

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large U . For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum r...

We compute the ground-state phase diagram of the Hubbard and frustrated Hubbard models on the square lattice with density matrix embedding theory using clusters of up to 16 sites. We provide an error model to estimate the reliability of the computations and complexity of the physics at different points in the diagram. We find superconductivity in the ground-state as well as competition between ...

This paper begins by analyzing the Fermi-Hubbard Hamiltonian, a hopping model for Fermions on a lattice, and the pathology of the model’s extreme cases is discussed. Finally, the usefulness of experiments with ultracold atoms for studying order in these systems is presented. William R. McGehee Long-Range Order in the Hubbard Model 2

We perform numerical simulations of the Hubbard model using the projector Quantum Monte Carlo method. A novel approach for nite size scaling is discussed. We obtain evidence in favor of d{wave superconductivity in the repulsive Hubbard model. For U = 4, T c is roughly estimated as T c 30 K.

Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an eff...

Mott-Hubbard metal-insulator transitions in N -fold degenerate Hubbard models are studied within the Gutzwiller approximation. For any rational filling with x (integer) electrons per site it is found that metal-insulator transition occurs at a critical correlation energy Uc(N,x) = Uc(N, 2N − x) = γ(N,x)|ǭ(N,x)|, where ǭ is the band energy per particle for the uncorrelated Fermi-liquid state and...