On the Supersymmetric XXX Spin Chains Associated to $$\mathfrak {gl}_{1|1}$$

@article{Lu2021OnTS,
  title={On the Supersymmetric XXX Spin Chains Associated to \$\$\mathfrak \{gl\}\_\{1|1\}\$\$},
  author={Kang Lu and Evgeny Mukhin},
  journal={Communications in Mathematical Physics},
  year={2021}
}
  • Kang Lu, E. Mukhin
  • Published 29 October 2019
  • Mathematics, Physics
  • Communications in Mathematical Physics
We study the $\mathfrak{gl}_{1|1}$ supersymmetric XXX spin chains. We give an explicit description of the algebra of Hamiltonians acting on any cyclic tensor products of polynomial evaluation $\mathfrak{gl}_{1|1}$ Yangian modules. It follows that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the Drinfeld polynomials. In particular our result implies that each common… 
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