Momentum-space instantons and maximally localized flat-band topological Hamiltonians
- Creators
- Jian, Chao-Ming
- Gu, Zheng-Cheng
- Qi, Xiao-Liang
Abstract
Recently, two-dimensional band insulators with a topologically nontrivial (almost) flat band in which integer and fractional quantum Hall effect can be realized without an orbital magnetic field have been studied extensively. Realizing a topological flat band generally requires longer range hoppings in a lattice Hamiltonian. It is natural to ask what is the minimal hopping range required. In this letter, we prove that the mean hopping range of the flat-band Hamiltonian with Chern number C_1 and total number of bands N has a universal lower bound of √4│C_1│/πN Furthermore, for the Hamiltonians that reach this lower bound, the Bloch wavefunctions of the topological flat band are instanton solutions of a CP^(N-1)equation image non-linear σ model on the Brillouin zone torus, which are elliptic functions up to a normalization factor.
Additional Information
© 2013 Wiley-VCH Verlag GmbH. Received 16 September 2012, revised 7 November 2012, accepted 8 November 2012. Published online 22 November 2012. CMJ and XLQ are supported by the David and Lucile Packard Foundation. ZCG is supported by Sherman Fairchild Foundation.Additional details
- Eprint ID
- 38810
- Resolver ID
- CaltechAUTHORS:20130605-104157548
- David and Lucile Packard Foundation
- Sherman Fairchild Foundation
- Created
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2013-06-05Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter