Prerequisite

The knowledge of linear algebra and basic methods of analysis (integral calculus, theory of the function of a complex variable, determinant identities) is required (but I will spend some time on recalling this material). The knowledge of representation theory of sl_2 is welcome. The familiarity with the basics of quantum mechanics(Hamiltonian, wavefunctions, Pauli matrices) will be useful throughout the whole course.

Abstract

Quantum algebras and the theory of their representations appear in many contexts of theoretical physics. This course will consider the Heisenberg integral chain one of their most famous examples. In the first part of the course, we will focus on describing the spin chain, its integrability, and its connection to other contexts. In the second part of the course, we will explore this model and its physical observables using the Bethe ansatz method.

Lecturer Intro.

Andrii Liashyk is a researcher in integrable systems, mainly quantum ones. He received his PhD degree from the Center for Advanced Studies at Skoltech in 2020. In 2022 he joined BIMSA as an Assistant Research Fellow.