Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators

TL;DR

This paper introduces an improved method for constructing many-body trial wave functions for fractional Chern insulators using a lattice-adapted Wannier basis, achieving high overlaps with exact ground states.

Contribution

It develops a gauge-fixed Wannier basis approach for lattice systems, fixing issues of continuum methods and accurately capturing fractional topological insulator ground states.

Findings

High overlap (>0.99) with exact ground states in several models

Constructed states are translationally invariant and preserve symmetries

Method applicable to large Hilbert spaces with up to 3x10^4 states

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.