GPP

Christian Hagendorf (UCLouvain) : On the supersymmetric eight-vertex model

Europe/Brussels
CYCL07 (Marc de Hemptinne)

CYCL07

Marc de Hemptinne

Description
Abstract : In this talk, I discuss the eight-vertex model with statistical weights $a, b, c, d$ related by $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$. In 2001, Stroganov conjectured that its transfer matrix for $L=2n+1$ vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly-degenerate special eigenvalue $\Theta_n = (a+b)^{2n+1}$. I show how to prove this conjecture. The proof utilises the supersymmetry of a related XYZ spin chain. The corresponding eigenstates are shown to be the spin-chain ground states. I describe how to compute some of their components. For $d=0$ and a suitable normalisation, they can be expressed by integer sequences that enumerate alternating sign matrices. Furthermore, I present an extension to open boundary conditions.