Mapping a fractional quantum Hall state to a fractional Chern insulator

TL;DR

This paper develops a variational method to accurately map fractional quantum Hall states to fractional Chern insulators, accounting for gauge freedom and optimizing interaction energy to improve the correspondence between these topological phases.

Contribution

It introduces a variational principle to fix gauge freedom in the FQH to FCI mapping, enhancing the accuracy of the wave function correspondence.

Findings

The gauge can be fixed by minimizing interaction energy.

The optimal gauge matches maximally localized Wannier functions.

The method improves the mapping for isotropic electron interactions.

Abstract

We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized \emph{two-dimensional} projected Wannier functions of a Landau level.