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Dimensional Hierarchy of Fermionic Interacting Topological Phases
Raquel Queiroz1, Eslam Khalaf1, Ady Stern2
1Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany.
Physical Review Letters
|November 26, 2016
Summary
Interactions can simplify complex topological phases. This study shows how interactions reduce the classification of fermionic symmetry-protected topological phases from an infinite set to a finite one.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Matter
Background:
- Symmetry-protected topological (SPT) phases are exotic states of matter characterized by topological invariants.
- Understanding the impact of interactions on these phases is crucial for a complete classification.
- Noninteracting fermionic SPT phases are classified by the group Z, posing challenges for interacting systems.
Purpose of the Study:
- To develop a method for classifying interacting fermionic SPT phases.
- To investigate how interactions modify the topological classification of these phases.
- To establish a general condition for interactions that drive SPT phases to a trivial state.
Main Methods:
- A dimensional reduction argument is employed to connect higher-dimensional topological properties to lower-dimensional defect properties.
- The topological character of a d-dimensional system is related to the number of zero-energy bound states at its surface's topological defects.
- A specific quartic interaction term is derived to render the system topologically trivial.
Main Results:
- A general condition for symmetry-preserving interactions that lead to topological triviality is established.
- The dimensional reduction successfully relates topological invariants to localized bound states.
- The classification of fermionic SPT phases is reduced from Z to Z_n in the presence of interactions, where n depends on the topological invariant.
Conclusions:
- Interactions significantly alter the classification of fermionic SPT phases, reducing the complexity.
- The derived method provides a pathway to understand and classify interacting topological phases.
- This work offers a new perspective on the interplay between topology, symmetry, and interactions in quantum matter.
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