Reviving the Lieb-Schultz-Mattis Theorem in Open Quantum Systems

Understand

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 letter, we propose that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to bath renders the system short-range correlated.
• Specifically, we argue that the entanglement spectrum cannot have a non-degenerate minimum, isolated by a gap from other states.