A tale of two Bethe ansätze

Antonio Lima-Santos; Rafael I. Nepomechie; Rodrigo A. Pimenta

doi:10.1088/1742-5468/aab851

A tale of two Bethe ansätze

Antonio Lima-Santos, Rafael I. Nepomechie, Rodrigo A. Pimenta

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	043107
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2018
Issue number	4
DOIs	https://doi.org/10.1088/1742-5468/aab851
State	Published - Apr 26 2018

Keywords

integrable spin chains and vertex models
quantum integrability (Bethe ansatz)

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Statistics, Probability and Uncertainty

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@article{487d5d596a674433b47be0409dd8463f,

title = "A tale of two Bethe ans{\"a}tze",

abstract = "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 ans{\"a}tze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.",

keywords = "integrable spin chains and vertex models, quantum integrability (Bethe ansatz)",

author = "Antonio Lima-Santos and Nepomechie, {Rafael I.} and Pimenta, {Rodrigo A.}",

note = "Funding Information: RP thanks Alexander Garbali for insightful discussions about the scalar product of 19-vertex models. This work was supported by the S{\~a}o 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.",

year = "2018",

month = apr,

day = "26",

doi = "10.1088/1742-5468/aab851",

language = "English (US)",

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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.

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)

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