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Topological Rényi entropy after a quantum quench.
Gábor B Halász1, Alioscia Hamma
1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5.
Physical Review Letters
|May 18, 2013
Summary
Topological order in quantum systems remains robust even after a quantum quench. Analyzing the toric-code model shows that topological Rényi entropy, a measure of topological order, returns to its initial value over time, demonstrating resilience.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
Background:
- Topological order characterizes exotic quantum phases of matter.
- Understanding the stability of topological order under dynamic perturbations is crucial.
Purpose of the Study:
- To analytically investigate the resilience of topological order in a quantum system after a quantum quench.
- To quantify the impact of external magnetic fields on topological properties.
Main Methods:
- The study employs the toric-code model as a representative system with topological order.
- Time evolution after a quantum quench is analyzed using topological Rényi entropy of order 2.
- Two types of quenches are considered: one with an exact solution and another requiring perturbation theory.
Main Results:
- The long-term time average of topological Rényi entropy in the thermodynamic limit is found to be invariant.
- This invariance holds true for both analytically solvable and perturbation theory-based quench scenarios.
- The findings indicate a consistent return of topological properties to their pre-quench state.
Conclusions:
- Topological order exhibits significant resilience against quantum quenches involving external magnetic fields.
- The results suggest that topological states can withstand a broad range of dynamic perturbations.
- This robustness has implications for fault-tolerant quantum computing and the study of topological phases.
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