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Symmetry protected fractional Chern insulators and fractional topological insulators | Yuan-Ming Lu
; Ying Ran
; | Date: |
1 Sep 2011 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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