- Author
- Pieter Claeys (UGent) , Stijn De Baerdemacker (UGent) and Dimitri Van Neck (UGent)
- Organization
- Abstract
- We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula. Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.
- Keywords
- ALGEBRAIC BETHE-ANSATZ, FORM-FACTORS, METALLIC GRAINS, WAVE-FUNCTIONS, BCS MODEL, EQUATIONS, CHAIN, BOUNDARIES, FRAMEWORK, SYSTEMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8545218
- MLA
- Claeys, Pieter, et al. “Inner Products in Integrable Richardson-Gaudin Models.” SCIPOST PHYSICS, vol. 3, no. 4, 2017, doi:10.21468/scipostphys.3.4.028.
- APA
- Claeys, P., De Baerdemacker, S., & Van Neck, D. (2017). Inner products in integrable Richardson-Gaudin models. SCIPOST PHYSICS, 3(4). https://doi.org/10.21468/scipostphys.3.4.028
- Chicago author-date
- Claeys, Pieter, Stijn De Baerdemacker, and Dimitri Van Neck. 2017. “Inner Products in Integrable Richardson-Gaudin Models.” SCIPOST PHYSICS 3 (4). https://doi.org/10.21468/scipostphys.3.4.028.
- Chicago author-date (all authors)
- Claeys, Pieter, Stijn De Baerdemacker, and Dimitri Van Neck. 2017. “Inner Products in Integrable Richardson-Gaudin Models.” SCIPOST PHYSICS 3 (4). doi:10.21468/scipostphys.3.4.028.
- Vancouver
- 1.Claeys P, De Baerdemacker S, Van Neck D. Inner products in integrable Richardson-Gaudin models. SCIPOST PHYSICS. 2017;3(4).
- IEEE
- [1]P. Claeys, S. De Baerdemacker, and D. Van Neck, “Inner products in integrable Richardson-Gaudin models,” SCIPOST PHYSICS, vol. 3, no. 4, 2017.
@article{8545218,
abstract = {{We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.
Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.}},
articleno = {{028}},
author = {{Claeys, Pieter and De Baerdemacker, Stijn and Van Neck, Dimitri}},
issn = {{2542-4653}},
journal = {{SCIPOST PHYSICS}},
keywords = {{ALGEBRAIC BETHE-ANSATZ,FORM-FACTORS,METALLIC GRAINS,WAVE-FUNCTIONS,BCS MODEL,EQUATIONS,CHAIN,BOUNDARIES,FRAMEWORK,SYSTEMS}},
language = {{eng}},
number = {{4}},
pages = {{34}},
title = {{Inner products in integrable Richardson-Gaudin models}},
url = {{http://doi.org/10.21468/scipostphys.3.4.028}},
volume = {{3}},
year = {{2017}},
}
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