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07 February 2025
 
  » arxiv » 1109.0226

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Symmetry protected fractional Chern insulators and fractional topological insulators
Yuan-Ming Lu ; Ying Ran ;
Date 1 Sep 2011
AbstractIn this paper we construct the wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) using the parton approach. We show that the lattice symmetry gives rise to many different FCI and FTI phases even with the same filling fraction $ u$ (and the same quantized Hall conductance $sigma_{xy}$ in FCI case). They have different symmetry-protected topological orders, which are characterized by different projective symmetry groups. We mainly focus on FCI phases which are realized in a partially filled band with Chern number one. The low-energy gauge groups of a generic $sigma_{xy}=1/mcdot e^2/h$ FCI wavefunctions are found to be either $SU(m)$ or discrete group $Z_m$, and in the latter case the associated low-energy physics are described by Chern-Simons-Higgs theories. We use our construction to compute the ground state degeneracy and extract the effective theory of gapless edge excitations. Examples of FCI/FTI wavefunctions on honeycomb lattice and checkerboard lattice are explicitly given. Possible non-Abelian FCI phases which may be realized in a partially filled band with Chern number two are discussed. Generic FTI wavefunctions in the absence of spin conservation are also presented whose low-energy gauge groups can be either $SU(m) imes SU(m)$ or $Z_m imes Z_m$. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations.
Source arXiv, 1109.0226
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