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We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a…
We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…
A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact…
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…
The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded…
From extensive numeric diagonalizations of the SU(3) Perk-Schultz Hamiltonian with a special value of the anisotropy and different boundary conditions, we have observed simple regularities for a significant part of its eigenspectrum. In…
The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe…
We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability…
We consider two particular 1D quantum many-body systems with local interactions related to the root system $C_N$. Both models describe identical particles moving on the half-line with non-trivial boundary conditions at the origin, and they…
We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial…
We construct an integrable Hubbard model with impurity site containing spin and charge degrees of freedom. The Bethe ansatz equations for the Hamiltonian are derived and two alternative sets of equations for the thermodynamical properties.…
The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$…
We construct a family of triatomic models for heteronuclear and homonuclear molecular Bose-Einstein condensates. We show that these new generalized models are exactly solvable through the algebraic Bethe ansatz method and derive their…
We have studied a simple effective model of charge ordered insulators. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interaction Wij (both: nearest-neighbor and…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a…
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the…
Calculating the ground state properties of a Hamiltonian can be mapped to the problem of finding the ground state of a smaller Hamiltonian through the use of embedding methods. These embedding techniques have the ability to drastically…
We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right $K$-matrices have an upper triangular form. We show that the main…