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Conformal Geometry Program Seminar: Luigi Cantini, ENS

Luigi Cantini, ENS

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.