Related papers: Exact solution of a quantum integrable system asso…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the…
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…
We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…
We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…
We propose an expression for the eigenvalues of the transfer matrix for the $U_q(B_n)$-invariant open quantum spin chain associated with the fundamental representation of $A^{(2)}_{2n}$. By assumption, the Bethe Ansatz equations are…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using…
We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based…
The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting $K$-matrices leading to four different types of…
We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra $su(4)$. By employing the algebraic Bethe ansatz, we determine the exact solution for the energy…
The transfer matrix of the general integrable open XXZ quantum spin chain obeys certain functional relations at roots of unity. By exploiting these functional relations, we determine the Bethe Ansatz solution for the transfer matrix…
We consider the open spin-s XXZ quantum spin chain with N sites and general integrable boundary terms for generic values of the bulk anisotropy parameter, and for values of the boundary parameters which satisfy a certain constraint. We…
We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to…
The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices…
Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which…
We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up.…
Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$…
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…
We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables…