Lieb-Schultz-Mattis Theorem in Open Quantum Systems

Understand

The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-body systems and plays a significant role in the Haldane gap phenomena and topological phases of matter.

• Here, we extend the LSM theorem to open quantum systems and establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry.
• Specifically, we demonstrate that the unique gapped steady state is prohibited when translation invariance and U (1) symmetry are simultaneously present for noninteger filling numbers.
• As an illustrative example, we find that no dissipative gap is open in the spin-1/2 dissipative Heisenberg model while a dissipative gap can be open in the spin-1 counterpart -- an analog of the Haldane gap phenomena in open quantum systems.