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Non-abelian quantum Hall effect in topological flat bands.
Yi-Fei Wang1, Hong Yao, Zheng-Cheng Gu
1Center for Statistical and Theoretical Condensed Matter Physics, and Department of Physics, Zhejiang Normal University, Jinhua 321004, China.
Physical Review Letters
|May 1, 2012
Summary
Researchers found evidence of a stable bosonic non-abelian quantum Hall effect in lattice models. This discovery, observed in topological flat bands, opens new avenues for topological quantum computing.
Area of Science:
- Condensed Matter Physics
- Quantum Hall Effect
- Topological Phases of Matter
Background:
- Recent theoretical work has predicted robust fractional topological phases that do not require magnetic fields.
- Topological flat bands in lattice models are promising candidates for realizing exotic quantum phenomena.
- The non-abelian quantum Hall effect is a key ingredient for fault-tolerant topological quantum computing.
Purpose of the Study:
- To search for experimental evidence of the non-abelian quantum Hall effect in lattice models with topological flat bands.
- To investigate the properties of bosonic systems in topological flat bands for potential quantum Hall states.
Main Methods:
- Extensive numerical studies were performed on the Haldane model.
- Three-body hard-core bosons were loaded into a topological flat band within the Haldane model.
- Analysis focused on ground state degeneracy, Chern number quantization, and energy spectrum of quasihole states.
Main Results:
- Convincing numerical evidence for a stable $\nu=1$ bosonic non-abelian quantum Hall effect was found.
- The observed ground states exhibited characteristic threefold quasidegeneracy on a torus, a quantized Chern number, and a robust spectrum gap.
- The spectrum for two-quasihole states also showed a finite energy gap, with state counting consistent with the Moore-Read pfaffian state.
Conclusions:
- The study provides strong numerical support for the existence of a bosonic non-abelian quantum Hall effect in a realistic lattice model.
- These findings demonstrate the feasibility of realizing non-abelian topological phases without external magnetic fields.
- The results pave the way for potential applications in topological quantum computing using bosonic systems.
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