Trial Wavefunctions for the Goldstone Mode in 𝜈=1/2+1/2 Quantum Hall Bilayers

Figure 2

Overlaps of the trial states for the Goldstone mode at 𝑑=0 (a) and 𝑑=3 (b) with the exact state, as in Figure 1, plotted here as a function of wavevector 𝑘∼𝐿/𝑁_𝜙/2. Despite the size of the Hilbert spaces increasing significantly between the smallest and largest system shown, the overlap remains roughly constant or maybe slightly increases with 𝑁. The region of high overlap extends roughly up to 𝑘≈2ℓ₀⁻¹. The failure of this approach for 𝑑=3 and 𝑁=12 is discussed in detail in the text.

(a)

(b)