Related papers: Bethe states for the two-site Bose-Hubbard model: …
The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz…
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant $R$-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix.…
For the one-dimensional Hubbard model with Aharonov-Bohm-type magnetic flux, we study the relation between its symmetry and the number of Bethe states. First we show the existence of solutions for Lieb-Wu equations with an arbitrary number…
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…
An exactly solvable strongly correlated electron model with two independent parameters is constructed in the frame of the quantum inverse scattering method, which can be seen as a generalization of the Bariev model. Through the Bethe ansatz…
We apply previous results on the O(N) Bethe Ansatz [1 to 3] to construct a general form factor formula for the O(N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the…
We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model.…
A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two…
The use of a single-qubit parametrized circuit as an Ansatz for the variational wave function in the calculation of the ground state energy of a quantum many-body system is demonstrated using the one-dimensional Bose-Hubbard model.…
We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$ superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their…
In this paper we derive out the exact solution of the SU(n) Hubbard model through the coordinate and the algebraic Bethe ansatz methods. The energy spectrum and the Bethe ansatz equations are obtained. Furthermore, we analysis the ground…
The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a…
We study quantum integrable models with $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. We analyze scalar products of generic Bethe vectors and obtain an explicit representation for them in terms of a sum…
Inspired by the increasing possibility of experimental control in ultracold atomic physics, we introduce a new Lax operator and use it to construct and solve models with two wells and two on-well states together with its generalization for…
A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis"…
A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…
The eigenvectors of the osp(1|2) invariant Gaudin hamiltonians are found using explicitly constructed creation operators. Commutation relations between the creation operators and the generators of the loop superalgebra are calculated. The…
We study quantum integrable GL(3)-based models with a trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation…
The electronic states of the Hubbard model are investigated by use of the Composite Operator Method. In addition to the Hubbard operators, two other operators related with two-site composite excitations are included in the basis. Within the…
We establish the method of Bethe ansatz for the XXZ type model obtained from the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is…