Related papers: Generating Series for Nested Bethe Vectors
For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is…
A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of…
Undirected neural sequence models such as BERT (Devlin et al., 2019) have received renewed interest due to their success on discriminative natural language understanding tasks such as question-answering and natural language inference. The…
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 Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…
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…
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.…
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…
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 study the $\mathfrak{gl}_{m|n}$ XXX spin chains defined on tensor products of highest $\mathfrak{gl}_{m|n}$-modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding…
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…
The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…
We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…
The $\rho\rho$ interaction and the corresponding dynamically generated bound states are revisited. We demonstrate that an improved unitarization method is necessary to study the pole structures of amplitudes outside the near-threshold…
Let $U^+_q$ denote the positive part of the quantized enveloping algebra $U_q(\widehat{\mathfrak{sl}}_2)$. The algebra $U^+_q$ has a presentation involving two generators $W_0$, $W_1$ and two relations, called the $q$-Serre relations. In…
We give new combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for the evaluation modules over the Yangian Y(gl_n). This paper extends the result for the Yangian Y(gl_4) established earlier in…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
The U_q(\hat{sl}(2)) Bethe equation is studied at q=0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and…
We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…