On integrable Floquet dynamics in the Temperley-Lieb dimer algebra

Fizicheskaya sistema nazyvayetsya integriruyemoy, yesli u yeyo Gamil'toniana imeyetsya polnyy nabor integralov dvizheniya (zaryadov). Yesli gamil'tonian sistemy zavisit ot vremeni periodicheski, to sistemu mozhno schitat' Floke-integriruyemoy, yesli naydotsya polnyy nabor integralov dvizheniya s tochnost'yu do perioda. V takikh sistemakh, v chastnosti, ne nablyudayetsya khaoticheskogo povedeniya. Mnogiye interesnyye modeli kvantovykh integriruyemykh tsepochek opisyvayutsya pri pomoshchi algebr Temperli-Liba, v svyazi s chem voznikayet interes vozmozhnosti opisaniya Floke-integriruyemosti v etikh algebrakh. V doklade eta problema budet reshena dlya chastnogo sluchaya dimernykh algebr Temperli-Liba: budut yavnym obrazom vypisany zaryady dlya Floke-dinamiki, yavnym obrazom nayden Floke-gamil'tonian, rassmotreno predstavleniye algebry simplekticheskimi fermionami i nayden sootvetstvuyushchiy spektr chastits. Ещё 846 / 5000 Результаты перевода A physical system is called integrable if its Hamiltonian has a complete set of integrals of motion (charges). If the Hamiltonian of a system depends periodically on time, then the system can be considered Floquet-integrable if there is a complete set of integrals of motion up to a period. In such systems, in particular, chaotic behavior is not observed. Many interesting models of quantum integrable chains are described using Temperley-Lieb algebras, in connection with which there is an interest in the possibility of describing Floquet-integrability in these algebras. In the talk, this problem will be solved for a special case of dimeric Temperley-Lieb algebras: the charges for the Floquet dynamics will be written out explicitly, the Floquet Hamiltonian is found explicitly, the representation of the algebra by symplectic fermions is considered, and the corresponding spectrum of particles is found.