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Rigorous Results on Topological Superconductivity with Particle Number Conservation
Matthew F Lapa1, Michael Levin1
1Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Physical Review Letters
|July 9, 2020
Summary
This study validates number-conserving models for topological superconductors, crucial for quantum computation. Rigorous methods show these realistic models retain key properties, unlike simplified mean-field approaches.
Area of Science:
- Condensed Matter Physics
- Quantum Computing
Background:
- Mean-field theories are widely used for topological superconductors and Majorana-based quantum computation.
- These theories often violate number conservation and assume short-range interactions, potentially misrepresenting real superconductors.
Purpose of the Study:
- To investigate topological properties using number-conserving models, addressing limitations of mean-field approaches.
- To establish reliable theoretical results for more realistic superconducting models.
Main Methods:
- Rigorous mathematical methods were employed.
- A number-conserving toy model of a topological superconducting wire was analyzed.
Main Results:
- The model demonstrated a finite energy gap within a fixed particle number sector.
- Long-range Majorana-like correlations were observed between the ends of an open wire.
- A change in ground state fermion parity was found for different boundary conditions.
Conclusions:
- Key topological properties of mean-field models are preserved in more realistic number-conserving models.
- This work supports the validity of number-conserving dynamics for topological superconductivity research.
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