21,941 research outputs found
Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
We introduce a Bloch-like basis in a C-component lowest Landau level
fractional quantum Hall (FQH) effect, which entangles the real and internal
degrees of freedom and preserves an Nx x Ny full lattice translational
symmetry. We implement the Haldane pseudopotential Hamiltonians in this new
basis. Their ground states are the model FQH wave functions, and our Bloch
basis allows for a mutatis mutandis transcription of these model wave functions
to the fractional Chern insulator of arbitrary Chern number C, obtaining wave
functions different from all previous proposals. For C > 1, our wave functions
are related to color-dependent magnetic-flux inserted versions of Halperin and
non-Abelian color-singlet states. We then provide large-size numerical results
for both the C = 1 and C = 3 cases. This new approach leads to improved
overlaps compared to previous proposals. We also discuss the adiabatic
continuation from the fractional Chern insulator to the FQH in our Bloch basis,
both from the energy and the entanglement spectrum perspectives.Comment: 6+epsilon pages, 2 figures. Published version. Added a discussion of
the emergent particle-hole symmetry in a Chern ban
Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
We propose an improved scheme to construct many-body trial wave functions for
fractional Chern insulators (FCI), using one-dimensional localized Wannier
basis. The procedure borrows from the original scheme on a continuum cylinder,
but is adapted to finite-size lattice systems with periodic boundaries. It
fixes several issues of the continuum description that made the overlap with
the exact ground states insignificant. The constructed lattice states are
translationally invariant, and have the correct degeneracy as well as the
correct relative and total momenta. Our prescription preserves the (possible)
inversion symmetry of the lattice model, and is isotropic in the limit of flat
Berry curvature. By relaxing the maximally localized hybrid Wannier orbital
prescription, we can form an orthonormal basis of states which, upon gauge
fixing, can be used in lieu of the Landau orbitals. We find that the exact
ground states of several known FCI models at nu=1/3 filling are well captured
by the lattice states constructed from the Laughlin wave function. The overlap
is higher than 0.99 in some models when the Hilbert space dimension is as large
as 3x10^4 in each total momentum sector.Comment: 36 pages, 13 figure
Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
In this paper we provide analytical counting rules for the ground states and
the quasiholes of fractional Chern insulators with an arbitrary Chern number.
We first construct pseudopotential Hamiltonians for fractional Chern
insulators. We achieve this by mapping the lattice problem to the lowest Landau
level of a multicomponent continuum quantum Hall system with specially
engineered boundary conditions. We then analyze the thin-torus limit of the
pseudopotential Hamiltonians, and extract counting rules (generalized Pauli
principles, or Haldane statistics) for the degeneracy of its zero modes in each
Bloch momentum sector.Comment: 19 pages, 5 figure
Braiding non-Abelian quasiholes in fractional quantum Hall states
Quasiholes in certain fractional quantum Hall states are promising candidates
for the experimental realization of non-Abelian anyons. They are assumed to be
localized excitations, and to display non-Abelian statistics when sufficiently
separated, but these properties have not been explicitly demonstrated except
for the Moore-Read state. In this work, we apply the newly developed matrix
product state technique to examine these exotic excitations. For the Moore-Read
and the Read-Rezayi states, we estimate the quasihole radii, and
determine the correlation lengths associated with the exponential convergence
of the braiding statistics. We provide the first microscopic verification for
the Fibonacci nature of the Read-Rezayi quasiholes. We also
present evidence for the failure of plasma screening in the non-unitary
Gaffnian wave function.Comment: 9 pages, 9 figures; published versio
Matrix product state representation of non-Abelian quasiholes
We provide a detailed explanation of the formalism necessary to construct
matrix product states for non-Abelian quasiholes in fractional quantum Hall
model states. Our construction yields an efficient representation of the wave
functions with conformal-block normalization and monodromy, and complements the
matrix product state representation of fractional quantum Hall ground states.Comment: 14 pages, 2 figures; published versio
- …