Lieb-Schultz-Mattis Theorem in Open Quantum Systems
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Summary
This summary is machine-generated.The Lieb-Schultz-Mattis theorem now applies to open quantum systems, revealing symmetry-based constraints on steady states and spectral gaps. This extends understanding of topological phases and Haldane gap phenomena in dissipative 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.
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