Speaker: Dr Jules Lamers
Affiliation: University of Melbourne

Abstract

I will introduce the landscape of quantum-integrable long-range spin chains, give an overview of the associated (quantum-)algebraic structures, and describe recent advances and open problems in the field.

Unlike for the traditionally studied nearest-neighbour Heisenberg spin chains, the exact solvability / quantum integrability of long-range spin chains exploits connections to quantum-many body systems of Calogero–Sutherland (or Ruijsenaars–Macdonald) type. For the so-called Haldane–Shastry spin chains this can be understood in terms of affine Hecke algebras, which yield Yangian (or quantum-loop) symmetries as well as eigenvectors featuring Jack (or Macdonald) polynomials. The Inozemtsev spin chain interpolates between Heisenberg and Haldane–Shastry. Its spectrum admits an exact characterisation in terms of eigenfunctions of the elliptic quantum Calogero–Sutherland model; here the underlying quantum-algebraic structure is not understood yet.

My talk is based on joint work with R. Klabbers (Nordita), with V. Pasquier and D. Serban (IPhT CEA/Saclay), and work in progress.

About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Travis Scrimshaw.

Venue

Priestley Building (67)
Room: 
442 (or via Zoom https://uqz.zoom.us/j/89058128574)