An algebraic approach to the Hubbard model

Marius de Leeuw; Vidas Regelskis

doi:10.1016/j.physleta.2015.12.013

An algebraic approach to the Hubbard model

Marius de Leeuw, Vidas Regelskis

Mathematics

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

Abstract

We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

Original language	English
Pages (from-to)	645-653
Journal	Phys. Lett. A
Volume	380
Issue number	5-6
DOIs	https://doi.org/10.1016/j.physleta.2015.12.013
Publication status	Published - 17 Dec 2015

Bibliographical note

10 pages; v2: references added

Keywords

math-ph
cond-mat.str-el
hep-th
math.MP
nlin.SI

Access to Document

10.1016/j.physleta.2015.12.013

Cite this

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title = "An algebraic approach to the Hubbard model",

abstract = "We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.",

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AU - Leeuw, Marius de

AU - Regelskis, Vidas

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PY - 2015/12/17

Y1 - 2015/12/17

N2 - We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

AB - We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

KW - math-ph

KW - cond-mat.str-el

KW - hep-th

KW - math.MP

KW - nlin.SI

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DO - 10.1016/j.physleta.2015.12.013

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SP - 645

EP - 653

JO - Phys. Lett. A

JF - Phys. Lett. A

IS - 5-6

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