**Title:** Finite Size Emptiness Formation Probability for the XXZ Spin Chain at $Delta=-1/2$

**Speaker:** Luigi Cantini, ENS

**Date:** Thursday, February 28, 2013

**Time:** 11:30am – 12:45pm

**Place:** Seminar Room 313, Simons Center

**Abstract: **Around 2000, Razumov and Stroganov have noticed that the wavefunction of the ground state of the XXZ spin chain at $Delta=-frac{1}{2}$ (a physical system whose study has a long history), displays several enumerations related to different classes of Alternating Sign Matrices (ASM) and more generically has a rich combinatorial structure. After recalling some of the main conjectures of R–S, we show how to exploit the relation between the solution of the level $1$ $\displaystyle{U_q(\hat{sl_2})}$ qKZ equation and the ground state of the inhomogeneous XXZ spin chain at $Delta=-frac{1}{2}$ in order to compute the exact Emptiness Formation Probability (EFP) of a periodic chain of finite length. The EFP turns out to have a “nice” factorized form and in certain cases reduces to enumerations of ASM or of certain symmetry classes of Plane Partitions.