One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

Abstract

We define a class of $Y(s{l}_{(m|n)})$ 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 one-dimensional vertex models.

References in corpus (20)

• Quantum Inverse Scattering Method and Correlation Functions
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• Yang-Baxter equation in spin chains with long range interactions
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Lattice Integrable Systems of Haldane-Shastry Type
• Baxter Q-Operators and Representations of Yangians
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Spectrum of a spin chain with inverse square exchange
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• New Family of Solvable 1D Heisenberg Models
• Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character
• Skew Young diagram method in spectral decomposition of integrable lattice models
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• On the level density of spin chains of Haldane--Shastry type
• Inozemtsev's hyperbolic spin model and its related spin chain

Cited by in corpus (6)

• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• The open Haldane-Shastry chain: thermodynamics and criticality
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum