Extended Data Fig. 4: System-size scaling.
From: Realization of a fractional quantum Hall state with ultracold atoms
Numerical system-size scaling of the observed FQH signatures for N = 2 particles in quadratic box potentials. Left panels show data for a 3 × 3 system and right panels show the behaviour when increasing the length L of the system. a, Energy-gap diagram with a gap closing at the flux ϕc/2π for tunnelling K/J = 1. For each system size, we compute the corresponding filling factor using νc = ρBulk/(ϕc/2π) (right panel). b, Doublon fraction with suppression at ϕc/2π. We extract the ratio \({p}_{{\rm{Doublon}}}^{{\rm{FQH}}}/{p}_{{\rm{Doublon}}}^{{\rm{Normal}}}\) from the doublon fraction \({p}_{{\rm{Doublon}}}^{{\rm{FQH}}}\) in the FQH state and \({p}_{{\rm{Doublon}}}^{{\rm{Normal}}}\) in the normal state, each extracted over an interval of Δϕ = 0.1 × ϕc. c, The reduced density correlations show already the vortex pattern for the 3 × 3 system (left panel). As the system size is increased, the correlations for neighbouring sites (|d| = 1), dark blue) approach zero and the correlations at a distance of 3lB (light blue, similar to Fig. 4c) stabilize at a value between one and two. d, Increase of the bulk density and extracted Hall conductivity σH/σ0 from a linear fit by means of Středa’s formula. When increasing the system size, the obtained Hall conductivity converges to σH/σ0 = 1/2.
