A Combinatorial Interpretation of the Scalar Products of State Vectors of Integrable Models

2014 ◽  
Vol 200 (6) ◽  
pp. 662-670 ◽  
Author(s):  
N. M. Bogoliubov ◽  
C. Malyshev
Keyword(s):  
Integrable Models ◽  
Combinatorial Interpretation ◽  
Scalar Products

scholarly journals ON THE CONSTRUCTION OF CORRELATION FUNCTIONS FOR THE INTEGRABLE SUPERSYMMETRIC FERMION MODELS

2006 ◽  
Vol 20 (05) ◽  
pp. 505-549 ◽  
Author(s):  
SHAO-YOU ZHAO ◽  
WEN-LI YANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Correlation Function ◽  
Physical Properties ◽  
Correlation Functions ◽  
Recent Progress ◽  
Integrable Models ◽  
Thermodynamical Limit ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Creation ◽  
Scalar Products

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the Uq(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

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 Highest coefficient of scalar products inSU(3)-invariant integrable models

2012 ◽  
Vol 2012 (09) ◽  
pp. P09003 ◽  
Author(s):  
S Belliard ◽  
S Pakuliak ◽  
E Ragoucy ◽  
N A Slavnov
Keyword(s):  
Integrable Models ◽  
Scalar Products

scholarly journals Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza
Keyword(s):  
Generating Functions ◽  
Combinatorial Interpretation ◽  
Hurwitz Numbers ◽  
Jacobi Ensemble ◽  
Matrix Ensembles ◽  
Wilson Polynomials ◽  
Unitary Ensemble ◽  
Topological Expansion

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

Sign in / Sign up

Export Citation Format

Share Document