scholarly journals Eigenvalue-based determinants for scalar products and form factors in Richardson–Gaudin integrable models coupled to a bosonic mode

2015 ◽  
Vol 48 (42) ◽  
pp. 425201 ◽  
Author(s):  
Pieter W Claeys ◽  
Stijn De Baerdemacker ◽  
Mario Van Raemdonck ◽  
Dimitri Van Neck
Keyword(s):  
Form Factors ◽  
Integrable Models ◽  
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 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 Angular quantization and form factors in massive integrable models

1998 ◽  
Vol 512 (3) ◽  
pp. 616-636 ◽  
Author(s):  
Vadim Brazhnikov ◽  
Sergei Lukyanov
Keyword(s):  
Form Factors ◽  
Integrable Models

scholarly journals Form factors inSU(3)-invariant integrable models

2013 ◽  
Vol 2013 (04) ◽  
pp. P04033 ◽  
Author(s):  
S Belliard ◽  
S Pakuliak ◽  
E Ragoucy ◽  
N A Slavnov
Keyword(s):  
Form Factors ◽  
Integrable Models

scholarly journals A NEW SET OF EXACT FORM FACTORS

1994 ◽  
Vol 09 (29) ◽  
pp. 5121-5143 ◽  
Author(s):  
FEODOR A. SMIRNOV
Keyword(s):  
Field Model ◽  
Central Charge ◽  
Form Factors ◽  
Present Form ◽  
Integrable Models ◽  
Chiral Field ◽  
Exact Form ◽  
Principal Chiral Field ◽  
Wide Range ◽  
Interesting Structure

We present form factors for a wide range of integrable models which include marginal perturbations of the SU(2) WZNZ model for arbitrary central charge and the principal chiral field model. The interesting structure of these form factors is discussed.

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