Advanced search
2 files | 1.33 MB Add to list

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

Author
Organization
Abstract
Starting from integrable su(2) (quasi-) spin Richardson-Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke-Jaynes-Cummings-Gaudin models and the two-channel (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke-Jaynes-Cummings-Gaudin models with the general results for RG XXZ models.
Keywords
scalar products, Richardson-Gaudin models, form factors, EXACTLY-SOLVABLE MODELS, ALGEBRAIC BETHE-ANSATZ, HAMILTONIANS, QUANTUM, SYSTEMS, integrable systems

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 679.87 KB
  • 15-JPhysA-draft-Claeys.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 652.45 KB

Citation

Please use this url to cite or link to this publication:

MLA
Claeys, Pieter et al. “Eigenvalue-based Determinants for Scalar Products and Form Factors in Richardson-Gaudin Integrable Models Coupled to a Bosonic Mode.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 48.42 (2015): n. pag. Print.
APA
Claeys, Pieter, De Baerdemacker, S., Van Raemdonck, M., & Van Neck, D. (2015). Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 48(42).
Chicago author-date
Claeys, Pieter, Stijn De Baerdemacker, Mario Van Raemdonck, and Dimitri Van Neck. 2015. “Eigenvalue-based Determinants for Scalar Products and Form Factors in Richardson-Gaudin Integrable Models Coupled to a Bosonic Mode.” Journal of Physics A-mathematical and Theoretical 48 (42).
Chicago author-date (all authors)
Claeys, Pieter, Stijn De Baerdemacker, Mario Van Raemdonck, and Dimitri Van Neck. 2015. “Eigenvalue-based Determinants for Scalar Products and Form Factors in Richardson-Gaudin Integrable Models Coupled to a Bosonic Mode.” Journal of Physics A-mathematical and Theoretical 48 (42).
Vancouver
1.
Claeys P, De Baerdemacker S, Van Raemdonck M, Van Neck D. Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2015;48(42).
IEEE
[1]
P. Claeys, S. De Baerdemacker, M. Van Raemdonck, and D. Van Neck, “Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 48, no. 42, 2015.
@article{6977296,
  abstract     = {Starting from integrable su(2) (quasi-) spin Richardson-Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke-Jaynes-Cummings-Gaudin models and the two-channel (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke-Jaynes-Cummings-Gaudin models with the general results for RG XXZ models.},
  articleno    = {425201},
  author       = {Claeys, Pieter and De Baerdemacker, Stijn and Van Raemdonck, Mario and Van Neck, Dimitri},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  keywords     = {scalar products,Richardson-Gaudin models,form factors,EXACTLY-SOLVABLE MODELS,ALGEBRAIC BETHE-ANSATZ,HAMILTONIANS,QUANTUM,SYSTEMS,integrable systems},
  language     = {eng},
  number       = {42},
  pages        = {29},
  title        = {Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode},
  url          = {http://dx.doi.org/10.1088/1751-8113/48/42/425201},
  volume       = {48},
  year         = {2015},
}

Altmetric
View in Altmetric
Web of Science
Times cited: