Finding local integrals of motion in quantum lattice models in the thermodynamic limit.

Accurate numerical studies typically involve a diagonalization procedure that can only be applied to small quantum systems. Consequently, thermodynamic limit results for generic quantum systems are very rare. During the talk I will demonstrate that identifying local integrals of motion (LIOMs) belongs to this rare class of problems [1]. LIOMs are essential for the long-time dynamics and thermalization of closed quantum systems. We derive a method that provides exact LIOMs for Hamiltonian systems and also for arbitrarily large quantum circuits. When applied to (more realistic) nearly integrable models, it provides slow modes and approximate relaxation times. Our approach can be applied to problems that are very demanding for other numerical methods, and the codes [2] demonstrate its technical simplicity.

[1] J. Pawłowski, J. Herbrych, and M. Mierzejewski Phys. Rev. B 112, 155130 (2025).

[2] J Pawłowski, J Herbrych, M Mierzejewski, (https://github.com/JakubPawlowskii/InfiniteLIOMs) (2025)