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.