TY - JOUR
T1 - A tale of two Bethe ansätze
AU - Lima-Santos, Antonio
AU - Nepomechie, Rafael I.
AU - Pimenta, Rodrigo A.
N1 - Funding Information:
RP thanks Alexander Garbali for insightful discussions about the scalar product of 19-vertex models. This work was supported by the São Paulo Research Foundation (FAPESP) and the University of Miami under the SPRINT grant #2016/50023-5. Additional support was provided by the Brazilian Research Council (CNPq) grant # 310625/2013-0 and FAPESP #2011/18729-1 (ALS), by a Cooper fellowship and a Fulbright Specialist grant (RN), and by FAPESP/ CAPES grant # 2017/02987-8 (RP). RN acknowledges the hospitality at UFSCar, ICTP-SAIFR and AIMS-SA. RP thanks the University of Miami for its warm hospitality.
Publisher Copyright:
© 2018 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2018/4/26
Y1 - 2018/4/26
N2 - We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ansätze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.
AB - We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ansätze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.
KW - integrable spin chains and vertex models
KW - quantum integrability (Bethe ansatz)
UR - http://www.scopus.com/inward/record.url?scp=85046776308&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85046776308&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/aab851
DO - 10.1088/1742-5468/aab851
M3 - Article
AN - SCOPUS:85046776308
VL - 2018
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
IS - 4
M1 - 043107
ER -