Wave Functions for Fractional Chern Insulators on Disk Geometry

TL;DR

This paper constructs and analyzes many-body wave functions for fractional Chern insulators on disk geometry, demonstrating high overlaps with exact states and reproducing edge excitation spectra consistent with chiral Luttinger liquid theory.

Contribution

It introduces a method to construct FCI/FQAH wave functions using GPP and Jack polynomials, achieving high accuracy and larger system sizes than previous approaches.

Findings

Wave-function overlap exceeds 0.97 with exact states.

Edge excitation spectra match chiral Luttinger liquid predictions.

Method allows analysis of larger lattice systems with more particles.

Abstract

Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena as the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states on the disk geometry with the aid of the generalized Pauli principle (GPP) and the Jack polynomials. Compared with the ground state by exact diagonalization method, the wave-function overlap is higher than $0.97$ even when the Hilbert space dimension is as large as $3\times10^6$. We also use the GPP and the Jack polynomials to construct edge excitations for the ferminoic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.