Ever since the first observation of Bose-Einstein condensation in 1990s, ultracold quantum gases have been subject intense research, providing a unique tool to understand behavior matter governed by laws mechanics. Ultracold bosonic atoms loaded an optical lattice are usually described Bose-Hubbard model or variant it. In addition common insulating and superfluid phases, other phases (such as d...

The five-band Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystal-field splitting is large, one may consider excitations confined to the lowest threefold-degenerate t2g orbital states. When the electron hopping matrix element (t) is much s...

We study the off-equilibrium dynamics of the infinite-dimensional Bose-Hubbard model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the ...

We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model. PACS: 75.10.Jm, 71.10.Fd, 05.30.Fk.