scholarly journals On determinant representations of scalar products and form factors in the SoV approach: the XXX case

2016 ◽  
Vol 49 (10) ◽  
pp. 104002 ◽  
Author(s):  
N Kitanine ◽  
J M Maillet ◽  
G Niccoli ◽  
V Terras
Keyword(s):  
Form Factors ◽  
Scalar Products

scholarly journals Nested Algebraic Bethe Ansatz in integrable models: recent results

2018 ◽  
Author(s):  
Stanislav Pakuliak ◽  
Eric Ragoucy ◽  
Nikita Slavnov
Keyword(s):  
Bethe Ansatz ◽  
General Expression ◽  
Monodromy Matrix ◽  
Form Factors ◽  
Integrable Models ◽  
Quantum Deformation ◽  
Algebraic Bethe Ansatz ◽  
Composite Models ◽  
Scalar Products

We review the recent results we have obtained in the framework of algebraic Bethe ansatz based on algebras and superalgebras of rank greater than 1 or on their quantum deformation. We present different expressions (explicit, recursive or using the current realization of the algebra) for the Bethe vectors. Then, we provide a general expression (as sum over partitions) for their scalar products. For some particular cases (in the case of gl(3)gl(3) or its quantum deformation, or of gl(2|1)gl(2|1)), we provide determinant expressions for the scalar products. We also compute the form factors of the monodromy matrix entries, and give some general methods to relate them. A coproduct formula for Bethe vectors allows to get the form factors of composite models.

scholarly journals On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model

2021 ◽  
Author(s):  
Hao Pei ◽  
Veronique Terras
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Separation Of Variables ◽  
Form Factors ◽  
Periodic Case ◽  
Matrix Elements ◽  
Heisenberg Chain ◽  
Xxz Model ◽  
Matrix Eigenvalues ◽  
Scalar Products

Abstract We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions, solution of a Baxter TQ-equation, which have double periodicity compared to the periodic case. We compute in this framework the scalar products of a particular class of separate states which notably includes the eigenstates of the transfer matrix. We also compute the form factors of local spin operators, i.e. their matrix elements between two eigenstates of the transfer matrix. We show that these quantities admit determinant representations with rows and columns labelled by the roots of the Q-functions of the corresponding separate states, as in the periodic case, although the form of the determinant are here slightly different. We also propose alternative types of determinant representations written directly in terms of the transfer matrix eigenvalues.

scholarly journals EXACT SOLUTION AT INTEGRABLE COUPLING OF A MODEL FOR THE JOSEPHSON EFFECT BETWEEN SMALL METALLIC GRAINS

2002 ◽  
Vol 16 (23) ◽  
pp. 3429-3438 ◽  
Author(s):  
JON LINKS ◽  
HUAN-QIANG ZHOU ◽  
ROSS H. MCKENZIE ◽  
MARK D. GOULD
Keyword(s):  
Josephson Effect ◽  
Form Factors ◽  
Cooper Pairs ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Pair Tunneling ◽  
Scalar Products ◽  
Metallic Grains ◽  
Integrable Coupling ◽  
Small Metallic Grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

THE STRUCTURE OF 6Li AND ITS COULOMB FORM FACTORS

1971 ◽  
Vol 32 (C5) ◽  
pp. C5b-269-C5b-270
Author(s):  
Kuniharu Kubodera
Keyword(s):  
Form Factors
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