Galois symmetry of the magnetic pentagonal ring within the XXX model
Prof. Tadeusz Lulek,ISQI, Faculty of Physics and Astronomy, Adam Mickiewicz University Poznań

Date, Time
04.12, 15:00 - 16:00

Spin chains are nowadays seen as quantum integrable systems, and thus can be useful in quantum information processing. Here we consider the system of N = 5 qubits, arranged into a regular ring, with isotropic nearest-neighbor interactions, within the XXX model. We first present a simple example of Galois symmetry within the picture of Bloch phases as cyclotomic numbers (i. e. primitive first roots of unity) for a pentagon. Then we sketch the physical status of the pentagonal ring as a quantum integrable system, the role of Baxter TQ relation and its linearized form in explanation of connection between Bethe roots of each highest weight eigenstate of the model and its integrability constants of motion. Finally, we analyze the Galois symmetry of the system of all Bethe roots on the generic star in the Brillouin zone of pentagon in the sector of two-magnon states. We demonstrate that the corresponding Galois group adequately describes the string structure of pentagonal eigenstates.

References:
[1] T. Lulek, M. Łabuz, J. Milewski, and R. Stagraczyński, Physica B,550,294-302(2018),
[2] T. Lulek, R. Stagraczyński, and M. Łabuz, Nucl. Phys. B, 991,116215(2023). [3] T. Lulek, M. Łabuz, J. Milewski, and R. Stagraczyński, Rep. Math. Phys. 91,345-357(2023).