Scalar products and norm of Bethe vectors for integrable models based on Uq ((gl)over-capm)

被引：13

作者：

Hutsalyuk, Arthur ^{[1
,2
]}

Liashyk, Andrii ^{[3
,4
,5
]}

Pakuliak, Stanislav Z. ^{[1
,6
]}

Ragoucy, Eric ^{[7
,8
]}

Slavnov, Nikita A. ^{[9
]}

机构：

[1] Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Reg, Russia

[2] Berg Univ Wuppertal, Fachbereich Phys C, D-42097 Wuppertal, Germany

[3] NAS Ukraine, Bogoliubov Inst Theoret Phys, Kiev, Ukraine

[4] Natl Res Univ, Higher Sch Econ, Fac Math, Moscow, Russia

[5] Skolkovo Inst Sci & Technol, Moscow, Russia

[6] JINR, Lab Theoret Phys, Dubna, Moscow Reg, Russia

[7] CNRS, Lab Phys Theor LAPTh, BP 110, F-74941 Annecy Le Vieux, France

[8] USMB, BP 110, F-74941 Annecy Le Vieux, France

[9] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

SCIPOST PHYSICS | 2018年 / 4卷 / 01期

关键词：

AFFINE ALGEBRA U-Q((GL)OVER-CAP(N)); DELTA-FUNCTION INTERACTION; QUANTUM INVERSE PROBLEM; INTERACTING BOSE-GAS; MANY-BODY PROBLEM; FORM-FACTORS; R-MATRIX; GL(M-VERTICAL-BAR-N) SYMMETRY; WAVE-FUNCTIONS; SYSTEM;

D O I：

10.21468/SciPostPhys.4.1.006

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra U-q((gl) over cap (m)). We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, whose factors are characterized by two highest coefficients. We provide different recursions for these highest coefficients. In addition, we show that when the Bethe vectors are on-shell, their norm takes the form of a Gaudin determinant.

引用

页数：30

共 15 条

[1] A REALIZATION OF THE ENVELOPING SUPERALGEBRA UQ((gl)over-capm|n)
Du, Jie
Fu, Qiang
Lin, Yanan
NAGOYA MATHEMATICAL JOURNAL, 2022, 247 : 516 - 551
[2] Bethe vectors of quantum integrable models based onUq ((gl)over-capN)
Pakuliak, S.
Ragoucy, E.
Slavnov, N. A.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (10)
[3] Scalar products of Bethe vectors in the models with gl(m|n) symmetry
Hutsalyuk, A.
Liashyk, A.
Pakuliak, S. Z.
Ragoucy, E.
Slavnov, N. A.
NUCLEAR PHYSICS B, 2017, 923 : 277 - 311
[4] Bethe vectors of GL(3)-invariant integrable models
Belliard, S.
Pakuliak, S.
Ragoucy, E.
Slavnov, N. A.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2013,
[5] On Bethe vectors in gl3-invariant integrable models
Liashyk, A.
Slavnov, N. A.
JOURNAL OF HIGH ENERGY PHYSICS, 2018, (06):
[6] Norm of Bethe vectors in models with gl(m|n) symmetry
Hutsalyuk, A.
Liashyk, A.
Pakuliak, S. Z.
Ragoucy, E.
Slavnov, N. A.
NUCLEAR PHYSICS B, 2018, 926 : 256 - 278
[7] Scalar products of Bethe vectors in models with gl(2| 1) symmetry 2. Determinant representation
Hutsalyuk, A.
Liashyk, A.
Pakuliak, S. Z.
Ragoucy, E.
Slavnov, N. A.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2017, 50 (03)
[8] GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
Pakuliak, Stanislav
Ragoucy, Eric
Slavnov, Nikita A.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2015, 11
[9] Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
Belliard, Samuel
Pakuliak, Stanislav
Ragoucy, Eric
Slavnov, Nikita A.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2013, 9
[10] A Combinatorial Interpretation of the Scalar Products of State Vectors of Integrable Models
Bogoliubov N.M.
Malyshev C.
Journal of Mathematical Sciences, 2014, 200 (6) : 662 - 670

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