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Warning: Cannot modify header information - headers already sent by (output started at /tmp/nav.php4v8maI:2) in /tmp/nav.php4v8maI on line 7 Seminare der Theoretischen Physik
Many properties of quantum systems can be obtained from a single energy eigenstate. For example, its entanglement entropy can be used to identify ergodic behavior. Additionally, in ergodic systems, a single eigenstate also encodes thermal properties. During the presentation, we will demonstrate that local integrals of motion (LIOMs), which lie at the heart of integrability, can also be estimated from a small number of eigenstates. Their number decreases with system size, becoming a vanishing fraction of the Hilbert space dimension in the thermodynamic limit. As a result, a small number of eigenstates is also sufficient to establish thermal properties of integrable systems. Interestingly, this does not extend to LIOMs arising solely from Hilbert space fragmentation. This represents one of the few fundamental differences known between integrability and Hilbert space fragmentation.
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)
