Fig. 3: Signatures of fermionic interaction terms.

Evolution of a L = 12 spin crystal with long-range interactions, initialized in a staggered spin state. a In the absence of Floquet fields (\(\bar{\eta }=0\)), the spin excitations quickly hop and thermalize. With full Floquet modulation (b \(\bar{\eta }=0.6\) and c \(\bar{\eta }=1\)), thermalization is partially suppressed and the edges become more protected. Simulation of the \(\bar{\eta }=0.6\) configuration (subplot b) of spins j = 1 (d), j = 4 (e) and j = 9 (f). Experimental data (black circle with error bars) agree well with a full simulation of an equivalent fermionic Hamiltonian containing interaction terms (green curve). Bars represent 1σ binomial uncertainties. For the bulk spins, the data does not agree with a long-range free-fermionic Hamiltonian (magenta curve). The dynamics of all spins are shown in Supplementary Fig. 1. These results are contrasted with short range spin models which are fully explained by free-fermionic evolution. See text and Supplementary Fig. 5.