Extended Data Fig. 2: Trotterization scheme.
From: Observation of Stark many-body localization without disorder
a, Numerics comparison of the imbalance dynamics for the averaged Hamiltonian of equation (13) (solid blue line) with the full Trotter evolution (dashed orange), for the case of an initial Néel state (N = 15) and parameters corresponding to the strongest experimental field gradient. b, Difference (averaged - Trotter) between the plots in a, showing that the Trotter error over experimental timescales is on the order of one percent. c, Experimental examples (top row) of continuous and Trotterized evolution, both at g/J0 = 1.5, compared to simulations (bottom row) using the (slightly different) parameters of the individual experimental realizations. Although the Trotterized evolution lasts nearly twice as much time in absolute units, since the averaged J0 is roughly half as large, it nonetheless shows a substantial reduction in decoherence and improvement in fidelity to the desired Hamiltonian. An initial state with one spin flip is chosen for this comparison, as it makes the effect of decoherence due to phonons more pronounced compared with a state near zero net magnetization.
