Dr. Ryszard Stagraczyński (Department of Physics and Medical Engineering, Rzeszów University of Technology
seminarium on-line, 28.05.2026, 15:00
Title: From Cyclic Groups to Baxter's Generalized Eigenvalue Problem: Decoding the Periodic Heisenberg XXX Model
Abstract:
Quantum integrable models are interesting tools in multiple subfields of physics. In this talk, I will consider a Heisenberg XXX chain with periodic boundary conditions. This translational symmetry generates cyclic groups C_N whose representations define quasimomenta. One can encode that by mapping the roots of unity to the invariant factors of the translation operator. This results in the decomposition of the state space into subspaces with fixed values of these quantum numbers [1]. The solutions may be obtained within the Algebraic Bethe Ansatz [2] formalism. Here, I will demonstrate the construction using the 'gear rack' approach [3]. Finally, we discuss the role of this symmetry for Baxter's generalized eigenvalue problem.
[1] T. Lulek, R. Stagraczyński, and M. Łabuz, Nucl. Phys. B, 991,116215(2023).
[2] L. D. Faddeev, How Algebraic Bethe Ansatz works for integrable model, arXiv:hep-th/9605187.
[3] R. Stagraczyński, T. Lulek, Computer Physics Communications, 2026, 110135, 10.1016/j.cpc.2026.110135.