Evolution of the optimal trial wave function with interactions in fractional Chern insulators

TL;DR

This study investigates how the optimal trial wave function for fractional Chern insulators varies with different electron-electron interactions, revealing that the gauge depends on the interaction form and differs from previously proposed gauges.

Contribution

It introduces a variational approach to determine the optimal gauge for trial wave functions under various interactions in fractional Chern insulators.

Findings

Wu et al.'s gauge closely matches the optimal gauge for mixed interactions.

Qi's gauge significantly differs from the optimal gauge across all interaction types.

The optimal gauge evolves with the interaction, especially when short-range components dominate.

Abstract

We show that the optimal trial wave function of a fractional Chern insulator depends on the form of its electron-electron interaction. The gauge of single particle Bloch bases for constructing the optimal trail wave function is obtained by applying the variational principle proposed by Zhang et al. [Phys. Rev. B 93, 165129 (2016)]. We consider a short-range interaction, the Coulomb interaction, and an interpolation between them, and determine the evolution of the optimal gauge with the different interactions. We compare the optimal gauge with those proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al. [Phys. Rev. B 86, 085129 (2012)], and find that Wu et al.'s gauge is close to the optimal gauge when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases. Both the gauges deviate significantly from the optimal gauge when the short-range component of the interaction becomes more prominent.