Fig. 5: Chiral current and density correlations across the phase diagram.
From: Strongly interacting Meissner phases in large bosonic flux ladders

a, Average chiral current as a function of K/J for U/J = 11.02(5) Hz and J/h = 71(1) Hz, prepared using the plaquette coupling sequence. The solid line is a fit of the expected chiral current from a DMRG simulation with scaling factor A as a free parameter, yielding A = 0.57(3). The blue-shaded area denotes the 1σ confidence interval of the fit. The dashed trace shows the non-interacting current, scaled down to the same amplitude, and the vertical line denotes the critical point without interactions. The top panel indicates the many-body gap across the phase diagram. Each data point is averaged over 80 repetitions and 14 ladders with 48 sites. b, Effective description of the flux ladder system in terms of two coupled Luttinger liquids (K ≪ J) and a one-dimensional spin chain (K ≫ J, U ≫ J). c, Enhancement of the average rung-wise density anti-correlations with increasing U and K/J. The orange-shaded areas indicate finite-temperature ED simulations (2 × 6 sites) of the density correlations from kBT = 0.5J (bottom line) to kBT = 1J (top line) for both interaction energies. Each data point was averaged over 30 repetitions and 14 ladders with 48 sites. The error bars denote the s.e.m., and if not visible, are smaller than the marker size.