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Universal Lower Bound on Topological Entanglement Entropy.
Isaac H Kim1, Michael Levin2, Ting-Chun Lin3,4
1Department of Computer Science, University of California, Davis, California 95616, USA.
Physical Review Letters
|November 5, 2023
Summary
Topological entanglement entropy (TEE) in 2D gapped systems has a spurious, non-negative contribution. This finding establishes the anyon theory prediction as a universal lower bound for TEE, enabling a circuit-invariant definition.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Topological Phases of Matter
Background:
- Two-dimensional gapped ground states are characterized by entanglement entropies obeying an area law.
- A constant correction term, the topological entanglement entropy (TEE), often reflects the universal properties of the topological phase.
- The TEE is known to vary even for states within the same phase if they are related by constant-depth quantum circuits.
Purpose of the Study:
- To investigate the nature of the "spurious" topological entanglement entropy.
- To determine if the TEE predicted by anyon theory serves as a universal lower bound.
- To develop a definition of TEE that is invariant under constant-depth quantum circuits.
Main Methods:
- Analysis of entanglement entropies in two-dimensional gapped ground states.
- Theoretical investigation of the difference between calculated TEE and anyon theory predictions.
- Formulation of a modified TEE definition invariant under constant-depth circuit transformations.
Main Results:
- The spurious contribution to the topological entanglement entropy is proven to be always non-negative.
- The value predicted by anyon theory provides a universal lower bound for the topological entanglement entropy.
- A new definition of TEE is proposed, which remains invariant under constant-depth quantum circuits.
Conclusions:
- The non-negativity of spurious TEE solidifies the anyon theory prediction as a fundamental lower bound.
- This work reconciles the apparent non-universality of TEE with the underlying topological order.
- The proposed invariant TEE definition offers a more robust characterization of topological phases.
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