Lieb-Schultz-Mattis Theorem in Open Quantum Systems.

Area of Science:

• Quantum Many-Body Physics
• Open Quantum Systems
• Condensed Matter Theory

Background:

• The Lieb-Schultz-Mattis (LSM) theorem constrains quantum many-body systems, crucial for understanding topological phases and the Haldane gap.
• Extending these constraints to open quantum systems is vital for describing realistic, interacting quantum matter under dissipation.

Purpose of the Study:

• To generalize the Lieb-Schultz-Mattis theorem to open quantum systems.
• To establish symmetry-based restrictions on the steady states and spectral gaps of Liouvillians.
• To explore implications for topological phases and Haldane gap analogs in dissipative systems.

Main Methods:

• Formulation of a generalized LSM theorem for open quantum systems.
• Analysis of Liouvillian properties based on symmetries like translation invariance and U(1) symmetry.
• Investigation of specific models, including dissipative Heisenberg models with different spin values.

Main Results:

• A unique gapped steady state is prohibited under translation invariance and U(1) symmetry for noninteger filling numbers.
• Dissipative gaps are shown to be absent in the spin-1/2 dissipative Heisenberg model but can exist in the spin-1 counterpart.
• The LSM constraint is linked to quantum anomalies in the dissipative form factor of Liouvillians and intrinsic open system symmetries.

Conclusions:

• The generalized LSM theorem provides fundamental constraints on open quantum systems, analogous to closed systems.
• This work unifies the understanding of topological phases and phenomena in both closed and open quantum systems.
• The findings offer new pathways for engineering and characterizing topological states in dissipative quantum devices.