Related papers: Bethe Ansatz solution of triangular trimers on the…
A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…
We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and…
A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the…
We show that a rectangle triangle random tiling with a tenfold symmetric phase is solvable by Bethe Ansatz. After the twelvefold square triangle and the eightfold rectangle triangle random tiling, this is the third example of a rectangle…
Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles…
The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…
Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…
It is shown that the square-triangle random tiling model is equivalent to an asymmetric limit of the three colouring model on the honeycomb lattice. The latter model is known to be the O(n) model at T=0 and corresponds to the integrable…
We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the…
We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…
We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact results for noninteracting hard-core dimers by both a very simple geometrical argument and a general…
We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…
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…
An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the…
Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the…
The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The…
In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a…
In a recent work Povolotsky provided a three-parameter family of stochastic particle systems with zero-range interactions in one dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding…
By means of an algebraic Bethe ansatz approach we study the Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors…