Simulating a Chern Insulator with C = $\pm$2 on Synthetic Floquet Lattice

TL;DR

This paper proposes a 4-band Floquet lattice model to simulate a Chern insulator with Chern number ±2, extending topological measurement methods and demonstrating potential for quantum simulation of complex topological phases.

Contribution

It introduces a novel 4-band Floquet lattice model for Chern insulators with C=±2 and adapts measurement techniques to verify topological properties.

Findings

Successfully simulated Chern number ±2 in Floquet lattice

Validated phase diagram with numerical simulations

Demonstrated potential for quantum topological matter simulation

Abstract

The synthetic Floquet lattice, generated by multiple strong drives with mutually incommensurate frequencies, provides a powerful platform for the quantum simulation of topological phenomena. In this study, we propose a 4-band tight-binding model of the Chern insulator with a Chern number C = $\pm$2 by coupling two layers of the half-BHZ lattice and subsequently mapping it onto the Floquet lattice to simulate its topological properties. To determine the Chern number of our Floquet-version model, we extend the energy pumping method proposed by Martin et al. [Phys. Rev. X 7, 041008 (2017)] and the topological oscillation method introduced by Boyers et al. [Phys. Rev. Lett. 125, 160505 (2020)], followed by numerical simulations for both methodologies. The simulation results demonstrate the successful extraction of the Chern number using either of these methods, providing an excellent prediction of the phase diagram that closely aligns with the theoretical one derived from the original bilayer half-BHZ model. Finally, we briefly discuss a potential experimental implementation for our model. Our work demonstrates significant potential for simulating complex topological matter using quantum computing platforms, thereby paving the way for constructing a more universal simulator for non-interacting topological quantum states and advancing our understanding of these intriguing phenomena.