Conserved quantities from Entanglement Hamiltonian

The description and understanding of integrability and chaos in isolated quantum many-body systems have been elusive for decades. It is generally believed that, as in classical mechanics, a set of conserved quantities plays a crucial role in determining whether a system is integrable or chaotic. In this work, we propose a novel method to identify quasi-local conserved quantities derived from the entanglement Hamiltonian by weakly coupling the system of interest with an identical auxiliary system. The number of independent conserved operators identified, as well as their relative weights, provides insight into whether the system exhibits integrability or chaos.