Fig. 3: Microscopic study of relaxation.
From: Observation of Hilbert space fragmentation and fractonic excitations in 2D
a, Fourier analysis of the average densities for the dimer state. The (π, π/2) Fourier component corresponding to the dimer state (dark blue) shows a fast decay, whereas the (0, π) Fourier component for the CDW along the vertical direction (light blue) increases before decreasing again, corresponding to the first hopping processes. b, Fourier analysis for the chequerboard state. The (π, π) component decays only slightly and remains the dominant component. c, Fourier analysis for the squares state. Both the (π/2, −π/2) and the (π/2, π/2) components decay quickly. The (π/2, −π/2) component, which describes decay in the direction of the equipotential lines, decays to a lower value and quickly becomes indistinguishable from the background, whereas the (π/2, π/2) component is above the background even at late times. For all initial states, all other components fall in-between the grey shaded areas describing the homogeneous background. Insets: the discrete two-dimensional Fourier transforms F(k) (orange colourmap) with Fourier modes k of the average densities (blue colourmap) for selected times. The coloured rectangles highlight the Fourier components shown in the plots. Error bars denote the standard error of the mean.
