Construction of Monodromy Matrix in the F - basis and scalar products in Spin chains
نویسنده
چکیده
We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the Monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.
منابع مشابه
Drinfel’d Twists and Algebraic Bethe Ansatz
We study representation theory of Drinfel’d twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R-matrices. We construct explicitly such factorizing F -matrices for irreducible finite n tensor products of the fundamental evaluation representations of the quantum affine algeb...
متن کاملخواص الکترونی یک زنجیر فیبوناچی
Using a tight-binding model and transfer-matrix technique, as well as Lanczos algorithm, we numerically investigate the nature of the electronic states and electron transmission in site, bond and mixing Fibonacci model chains. We rely on the Landauer formalism as the basis for studying the conduction properties of these systems. Calculating the Lyapunov exponent, we also study the localization...
متن کاملSolution of the quantum inverse problem
We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the classical inverse scattering transform. It applies to fundamental spin chains, such as the XYZ chain, and to a number of important exactly solvable models of strongly correlated electrons, such as the super...
متن کاملAn efficient Imperialistic Competitive Algorithm for the closed-loop supply chains considering pricing for product, and fleet of heterogeneous vehicles
This paper investigates a pricing multi-period, closed-loop supply chains (CLSCs) with two echelons of producers and customers. Products are delivered to customers might be defective which are picked up and gathered in the collection center and will be fixed if it is possible and will be returned to the chain. Otherwise, they are sold as waste. This problem is determining price and distributio...
متن کاملTheoretical study of - stacking interactions in substituted-coronene||cyclooctatetraene complexes: A system without direct electrostatic effects of substituents
Stability of the ;-; stacking interactions in the substituted-coronene||cyclooctatetraene complexes wasstudied using the computational quantum chemistry methods (where || denotes ;–; stackinginteraction, and substituted-coronene is coronene which substituted with four similar X groups; X =OH, SH, H, F, CN, and NO). There are meaningful correlations between changes of geometricalparameters and t...
متن کامل