Fig. 1. Emergent double-well potential.

Calculated spin excitation probability after a quantum quench. (A) The spin chain starts with a single-spin excitation on the left end in an effective double-well potential, U_eff, whose barrier height is determined by the range α of the interactions. The black dots represent the positions of the ions, whereas the red dots represent the simulated spin excitation probabilities. (B) For short-range interactions (α = 1.33), we map the system to a particle in a 1D square well, where the excitation becomes symmetrically distributed across the chain as predicted by the GGE, ${\langle {\mathrm{\sigma }}_{\mathit{i}}^{\mathit{z}}\rangle }_{\text{GGE}}$. (D) However, for long-range interactions (α = 0.55), there is an emergent double-well potential, which prevents the efficient transfer of the spin, and the excitation location retains memory of the initial state, in contrast to ${\langle {\mathrm{\sigma }}_{\mathit{i}}^{\mathit{z}}\rangle }_{\text{GGE}}$. (C) The double-well gives rise to near-degenerate eigenstates as α is decreased, as seen in the calculated energy difference between all pairs of eigenstates versus α. The height of the plot quantifies the off-diagonal density matrix elements of the initial state.