Abstract:
In closed systems, the celebrated Lieb-Schultz-Mattis (LSM) theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetry cannot have a non-degenerate gapped ground state. However, the applicability of this theorem is diminished when the system interacts with a bath and loses its energy conservation. In this talk, I will show that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to bath renders the system short-range correlated. Compared with the original LSM theorem which primarily addresses UV--IR correspondence, our findings unveil that the UV data and topological constraints also have a pivotal role in shaping the entanglement in open quantum many-body systems.