Our monthly meeting will take place on Monday the 31st of April, from 4pm to 6pm (Central European Time). Our speakers will be Frank Göhmann and Luigi Cantini. The zoom link will be sent to the members of the projects through the mailing list. If you are interested in participating and you are not a PIICQ participant, please register sending us an email!
First talk by Frank Göhmann at 4pm
Title: Dynamical correlation functions of the Heisenberg-Ising antiferromagnet.
Abstract: IScattering experiments and transport experiments measure the dynamical response of matter systems to small perturbation of their equilibrium states. In quantum statistical mechanics this response is expressed in terms of dynamical correlation functions. Those are notoriously hard to calculate if interaction comes into play. We report recent progress on the calculation of the dynamical two-point functions of the Heisenberg-Ising chain in its massive antiferromagnetic parameter regime. We have expressed the longitudinal two-point function by a series of multiple integrals in which the integrands are known special functions of q-hypergeometric and q-gamma type. This will allow us to perform a numerical and asymptotic analysis in a mathematically well-defined framework. In this talk we describe our result as well as some of the physical and the methodological background.
Second talk by Andrei Prokhorov at 5pm
Title: Boundary emptiness formation probabilities in the six-vertex model at ∆ =−1/2.
Abstract: Since the seminal work of Razumov and Stroganov, we know that several zero temperature and finite size correlation functions of the XXZ spin-chain at Δ=-1/2, for specific boundary conditions, have (conjectural and sometime proven) closed exact formulas, often involving enumerations of combinatorial objects such as Alternating Sign Matrices or Plane Partitions. In this talk, after briefly reviewing some of the relevant background, we shall present new results obtained in collaboration with C. Hagendorf and A. Morin-Duchesne, concerning the overlap of the Δ=-1/2 XXZ spin-chain ground states with particular factorized states. Such overlaps have a nice interpretation in terms of the six-vertex model on a semi-infinte cylinder with free boundary conditions, as the expectation value of a string of polarized edges located at the edge of the cylinder.