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 inThe journal of high energy physics Vol. 2020; no. 5; pp. 1 - 35
Main Authors Robertson, Niall F., Pawelkiewicz, Michal, Jacobsen, Jesper Lykke, Saleur, Hubert
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020
Springer Nature B.V
Springer
SpringerOpen
Subjects
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
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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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.
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
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CitedBy_id crossref_primary_10_1007_JHEP08_2020_069
crossref_primary_10_1007_JHEP03_2022_175
crossref_primary_10_1007_JHEP04_2022_101
crossref_primary_10_1016_j_nuclphysb_2022_115799
crossref_primary_10_1007_JHEP02_2021_180
crossref_primary_10_1007_JHEP11_2023_095
crossref_primary_10_1007_JHEP01_2022_070
crossref_primary_10_1007_JHEP03_2021_089
crossref_primary_10_1088_1751_8121_acb29f
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Issue 5
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
Language English
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PublicationTitle The journal of high energy physics
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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
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