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 $\mathbb{Z}_3$ 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 $\mathbb{Z}_3$ 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