Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

Norms of Bethe wave functions for the nonlinear Schrödinger model of spin-1/2 particles

Gen-Di Pang, Fu‐Cho Pu, Bao‐Heng Zhao

Published Oct 1, 1990• 6 citations
Publisher

Abstract

A formula for scalar products of Bethe wave functions in the nonlinear Schrödinger model of spin- (1)/(2) particles is proposed. It is shown, in addition, that one can replace conjugate states by dual eigenfunctions to calculate correlation functions for integrable systems.
DOI
10.1063/1.528993

Related papers

Direct proof for the Scalar Product with Bethe eigenstate in Spin chains

А. А. Овчинников

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state.

arXiv:math-ph/0012042•Dec 22, 2000•0 citations

Slavnov and Gaudin–Korepin formulas for models without U (1) symmetry: the XXX chain on the segment

S. Belliard, Rodrigo A. Pimenta

Abstract We consider the isotropic spin Heisenberg chain with the most general integrable boundaries. The scalar product between the on-shell Bethe vector and its off-shell dual, obtained by means of the modified algebraic Bethe ansatz, is given by a modified Slavnov formula. The corresponding Gaudin–Korepin formula, i.e., the square of the norm, is also obtained.

arXiv:1507.03242•Journal of Physics A Mathematical and Theoretical•Mar 18, 2016•18 citations

Form factors of the operators at the boundary in quantum nonlinear Schr?dinger model

Yanshen Wang, Xuewen Yan, 西安交通大学应用物理系,西安 710049

For the nonlinear Schrdinger model with an integrable open boundary, the scalar products of Bethe eigenstates and form factors of operators at the boundary are calculated. The results are represented as determinants of usual functions with parameters of the model.

Acta Physica Sinica•Jan 1, 2006•0 citations

Scalar product for the XXZ spin chain with general integrable boundaries *

S. Belliard, Rodrigo A. Pimenta, Nikita A Slavnov

Abstract We calculate the scalar product of Bethe states of the XXZ spin- 1 2 chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q -Pochhammer polynomials of the boundary couplings.

arXiv:2103.12501•Journal of Physics A Mathematical and Theoretical•Jul 14, 2021•13 citations

Nonlinear integral equations and determinant formulae of the openXXZspin chain

Alexander Seel, Tobias Wirth

We derive a nonlinear integral equation for the Bethe ansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with the known determinant formula of norms and scalar products.

arXiv:0808.2108•Journal of Physics A Mathematical and Theoretical•Feb 18, 2009•1 citation

Semiclassical expansion of the Bethe scalar products in the XXZ spin chain

Constantin Babenko

In this note we adress the problem of performing the semiclassical expansion of the scalar product of Bethe states in the case of the XXZ spin chain. Our approach closely follows the one developped in [1]: after expressing the scalar products in terms of a central quantity - the B functional, we reinterpret it as a grand partition function of a gas of particles with pairwise interaction potential. This work has been done as part of the author's master thesis under the supervision of Ivan Kostov and Didina Serban at Institut de Physique Théorique (CEA Saclay) in September 2015 - February 2016, and present a consice summary of the results obtained at that time.

arXiv:1703.01123•Mar 3, 2017•2 citations
Abstract We calculate the scalar product of Bethe states of the XXZ spin- 1 2 chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q -Pochhammer polynomials of the boundary couplings.
In this note we adress the problem of performing the semiclassical expansion of the scalar product of Bethe states in the case of the XXZ spin chain. Our approach closely follows the one developped in [1]: after expressing the scalar products in terms of a central quantity - the B functional, we reinterpret it as a grand partition function of a gas of particles with pairwise interaction potential. This work has been done as part of the author's master thesis under the supervision of Ivan Kostov and Didina Serban at Institut de Physique Théorique (CEA Saclay) in September 2015 - February 2016, and present a consice summary of the results obtained at that time.