Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

TL;DR

This paper investigates how tuning hopping anisotropy in fractional Chern insulators can adiabatically connect a trivial charge density wave state to a topologically nontrivial FCI state, aiding their preparation in quantum simulators.

Contribution

It introduces a method to prepare FCIs via adiabatic evolution from a charge density wave state by tuning hopping anisotropy, supported by analytical and numerical analysis.

Findings

Adiabatic path connects CDW to FCI state.

Scaling of the excitation gap supports large FCI preparation.

Numerical simulations confirm the analytical predictions.

Abstract

We explore the quasi one-dimensional (thin torus, or TT) limit of fractional Chern insulators (FCIs) as a starting point for their adiabatic preparation in quantum simulators. Our approach is based on tuning the hopping amplitude in one direction as an experimentally amenable knob to dynamically change the effective aspect ratio of the system. Similar to the TT limit of fractional quantum Hall (FQH) systems in the continuum, we find that the hopping-induced TT limit adiabatically connects the FCI state to a trivial charge density wave (CDW) ground state. This adiabatic path may be harnessed for state preparation schemes relying on the initialization of a CDW state followed by the adiabatic decrease of a hopping anisotropy. Our findings are based on the calculation of the excitation gap in a number of FCI models, both on a lattice and consisting of coupled wires. By analytical calculation of the gap in the limit of strongly anisotropic hopping, we show that its scaling is compatible with the preparation of large size FCIs for sufficiently large hopping anisotropy. Our numerical simulations in the framework of exact diagonalization explore the full anisotropy range to corroborate these results.