The Bose-Hubbard hamiltonian will be introduced and justified as an effective description of some relevant physical systems (dilute alkali gases in optical lattices, arrays of Josephson junctions). I will also show a mean field theory solution and the resulting phase diagram. Finally, I will describe in detail one of the more important experiments with an optical lattice of Rb atoms. 1. The Bos...

The Hubbard model with an additional bond-charge interaction X is solved exactly in one dimension for the case t = X where t is the hopping amplitude. In this case the number of doubly occupied sites is conserved. In the sector with no double occupations the model reduces to the U = ∞ Hubbard model. In arbitrary dimensions the qualitative form of the phase diagram is obtained. It is shown that ...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

2 Contents Introduction iii 1 Ultracold atoms on optical lattices and the dirty boson problem 1 1.

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 ...

In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential V at the lattice boundary. Such thresholdless surface states, which can be referred to as Tamm-Hubbard BIC states, exist provided that the ...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...