Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators

Abstract

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.

36 pages, 13 figures

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
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• High temperature fractional quantum Hall states
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• Fractional Quantum Hall States and Jack Polynomials
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
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• Jacobi Theta-functions and Discrete Fourier Transforms

Cited by in corpus (13)

• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Adiabatic continuity between Hofstadter and Chern insulator states
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Interacting bosons in topological optical flux lattices
• Generalized Bloch theorem and topological characterization
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing