2013/04/30 by Jan Carl Budich, Eddy Ardonne
Materials Science · Mathematics · Physics and Astronomy · #Berry connection and curvature #Degenerate energy levels #Electron #Fractional quantum Hall effect #Geometric phase #Graphene research and applications #Ground state #Mathematics #Phase (matter) #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Quantum spin Hall effect #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.88.035139
published as Phys. Rev. B 88, 035139 (2013) · Final version
arxiv created 2013/07/29 · openalex publication_date 2013/07/29 · arxiv updated 2013/07/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a topologically nontrivial flat-band structure in one spatial dimension in the presence of nearest- and next-nearest-neighbor Hubbard interaction. The noninteracting band structure is characterized by a symmetry-protected topologically quantized Berry phase. At certain fractional fillings, a gapped phase with a filling-dependent ground-state degeneracy and fractionally charged quasiparticles emerges. At filling (1)/(3), the ground states carry a fractional Berry phase in the momentum basis. These features at first glance suggest a certain analogy to the fractional quantum Hall scenario in two dimensions. We solve the interacting model analytically in the physically relevant limit of a large band gap in the underlying band structure, the analog of a lowest Landau level projection. Our solution affords a simple physical understanding of the properties of the gapped interacting phase. We pinpoint crucial differences to the fractional quantum Hall case by studying the Berry phase and the entanglement entropy associated with the degenerate ground states. In particular, we conclude that the ``fractional topological phase in one-dimensional flat bands'' is not a one-dimensional analog of the two-dimensional fractional quantum Hall states, but rather a charge density wave with a nontrivial Berry phase. Finally, the symmetry-protected nature of the Berry phase of the interacting phase is demonstrated by explicitly constructing a gapped interpolation to a state with a trivial Berry phase.