Integrable boundary conditions in the antiferromagnetic Potts model
A bstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D 2 2 Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latt...
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Published in | The journal of high energy physics Vol. 2020; no. 5; pp. 1 - 35 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
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Springer Berlin Heidelberg
01.05.2020
Springer Nature B.V Springer SpringerOpen |
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Abstract | A
bstract
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine
D
2
2
Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known
K
-matrices of the
D
2
2
model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed. |
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AbstractList | A
bstract
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine
D
2
2
Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known
K
-matrices of the
D
2
2
model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed. We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D22 Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K -matrices of the D22 model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed. Abstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D 2 2 $$ {D}_2^2 $$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K -matrices of the D 2 2 $$ {D}_2^2 $$ model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed. We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $ {D}_2^2 $ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K -matrices of the $ {D}_2^2 $ model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed. |
ArticleNumber | 144 |
Author | Saleur, Hubert Pawelkiewicz, Michal Robertson, Niall F. Jacobsen, Jesper Lykke |
Author_xml | – sequence: 1 givenname: Niall F. surname: Robertson fullname: Robertson, Niall F. email: niall-fergus.robertson@ipht.fr organization: Université Paris Saclay, CNRS, CEA, Institut de Physique Théorique – sequence: 2 givenname: Michal surname: Pawelkiewicz fullname: Pawelkiewicz, Michal organization: Université Paris Saclay, CNRS, CEA, Institut de Physique Théorique – sequence: 3 givenname: Jesper Lykke surname: Jacobsen fullname: Jacobsen, Jesper Lykke organization: Université Paris Saclay, CNRS, CEA, Institut de Physique Théorique, Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Université, École Normale Supérieure, CNRS, Laboratoire de Physique (LPENS) – sequence: 4 givenname: Hubert surname: Saleur fullname: Saleur, Hubert organization: Université Paris Saclay, CNRS, CEA, Institut de Physique Théorique, Department of Physics and Astronomy, University of Southern California |
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Keywords | Lattice Integrable Models Conformal Field Theory Bethe Ansatz boundary condition algebra: Lie model: integrability Potts model staggered affine model: vertex algebra: Temperley-Lieb twist K-matrix |
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Snippet | A
bstract
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine
D
2
2
Lie algebra.... We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D22 Lie algebra. Using the known... We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $ {D}_2^2 $ Lie algebra. Using... Abstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D 2 2 $$ {D}_2^2 $$ Lie... |
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SubjectTerms | Antiferromagnetism Bethe Ansatz Boundary conditions Classical and Quantum Gravitation Conformal Field Theory Elementary Particles Free boundaries General Physics High energy physics Lattice Integrable Models Lie groups Mapping Mathematical Physics Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory String Theory |
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Title | Integrable boundary conditions in the antiferromagnetic Potts model |
URI | https://link.springer.com/article/10.1007/JHEP05(2020)144 https://www.proquest.com/docview/2407214278 https://hal.science/hal-02518080 https://doaj.org/article/93ebd9e11f3646afa4192986c6a72dec |
Volume | 2020 |
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