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Topological boundaries and bulk wavefunctions in the Su-Schreiffer-Heeger model
David S Simon1,2, Shuto Osawa2, Alexander V Sergienko2,3
1Department of Physics and Astronomy, Stonehill College, 320 Washington Street, Easton, MA 02357, United States of America.
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 14, 2018
Summary
Quantum walks in topological lattices show that boundary properties can localize wavefunctions. This topological boundary effect suppresses transitions, enabling potential information processing applications.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Topological Materials
Background:
- The Su-Schreiffer-Heeger model describes topological phases in one-dimensional systems.
- Quantum walks are a quantum analogue of classical random walks, with applications in quantum computation.
- Topological boundaries can exhibit unique physical phenomena due to abrupt changes in system properties.
Purpose of the Study:
- To investigate the impact of topological boundaries on bulk wavefunctions in a 1D quantum walk.
- To analyze the behavior of wavefunctions at interfaces between different topological phases.
- To explore the potential for wavefunction localization and its applications.
Main Methods:
- Utilizing the Su-Schreiffer-Heeger model for a 1D lattice.
- Constructing exact solutions for wavefunctions across topological boundaries.
- Calculating reflection and transmission coefficients as a function of hopping parameters.
Main Results:
- Wavefunction behavior at topological boundaries was precisely modeled.
- Reflection and transmission coefficients were quantified.
- Specific parameter ranges allow for significant suppression of transmission, leading to wavefunction localization.
Conclusions:
- Topological boundaries can effectively localize bulk wavefunctions within distinct topological regions.
- The 'topologically-assisted' suppression of transitions offers potential for information processing.
- Understanding these boundary effects is crucial for designing novel quantum devices.
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