### Abstract

We define a class of Y (sl_{(m{pipe}n)}) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with onedimensional vertex models.

Original language | English |
---|---|

Article number | 091 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 6 |

DOIs | |

Publication status | Published - Dec 1 2010 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*,

*6*, [091]. https://doi.org/10.3842/SIGMA.2010.091

**One-Dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.** / Basu-Mallick, Bireswar; Bondyopadhaya, Nilanjan; Hikami, Kazuhiro.

Research output: Contribution to journal › Article

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 6, 091. https://doi.org/10.3842/SIGMA.2010.091

}

TY - JOUR

T1 - One-Dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains

AU - Basu-Mallick, Bireswar

AU - Bondyopadhaya, Nilanjan

AU - Hikami, Kazuhiro

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We define a class of Y (sl(m{pipe}n)) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with onedimensional vertex models.

AB - We define a class of Y (sl(m{pipe}n)) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with onedimensional vertex models.

UR - http://www.scopus.com/inward/record.url?scp=84896064199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896064199&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2010.091

DO - 10.3842/SIGMA.2010.091

M3 - Article

VL - 6

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 091

ER -