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Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
Flore K Kunst1, Elisabet Edvardsson1, Jan Carl Budich2
1Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden.
Physical Review Letters
|August 8, 2018
Summary
Non-Hermitian systems challenge bulk-boundary correspondence. A new framework using biorthogonal quantum mechanics reveals how boundary states connect to bulk phase transitions, enabling generalized correspondence in open systems.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Topological Materials
Background:
- Non-Hermitian systems deviate from standard bulk-boundary correspondence.
- Bulk invariants fail to predict boundary states in these systems.
- Boundary states appear/disappear away from bulk gap closings.
Purpose of the Study:
- To establish a comprehensive framework for understanding non-Hermitian systems.
- To reconcile the behavior of boundary states with bulk properties.
- To generalize the bulk-boundary correspondence.
Main Methods:
- Utilizing the framework of biorthogonal quantum mechanics.
- Analyzing the biorthogonal density of left and right eigenstates.
- Developing a quantized biorthogonal polarization for open boundary systems.
Main Results:
- Biorthogonal density bridges bulk and boundary physics during phase transitions.
- A generalized bulk-boundary correspondence is established.
- Phase diagrams for open boundary models (e.g., non-Hermitian Su-Schrieffer-Heeger, Chern insulators) are derived.
Conclusions:
- Biorthogonal quantum mechanics provides a unified view of non-Hermitian systems.
- The developed framework accurately predicts phase transitions and boundary phenomena.
- This work offers new tools for studying topological phases in open quantum systems.
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