Fig. 4: Dynamics of fractonic excitations (positive defect).

a, Schematic of the spreading of the defect atom (filled green circle) to first order, which can move by forming doublons (dark-green shaded area). On short timescales (to first order), the associated defect hole (dashed circle) is stuck. b, Anisotropic spreading of the defect. The spreading of the defect can be observed in the occupations (owing to parity projection) and more clearly in the difference plots when subtracting the time-evolved reference chequerboard (CHB) background. Theory calculations are shown for comparison (Methods). The motion of the defect atom is restricted to a narrow stripe, along which it can move in only one direction. c, Diagonal sums over the reference-subtracted occupations. Orthogonal to the equipotential lines (left), the defect atom cannot spread, whereas parallel to the equipotential lines (right), it shows asymmetric propagation on the subdimensional manifold. Grey lines are guides to the eye, based on the points (sampled every 0.25 t/τ) where the theory calculations (green solid lines) exceed a value larger than 0.05. The coloured arrows show the direction of the summation of the diagonals, as indicated by the insets in the bottom, rightmost plot in b. Error bars denote the standard error of the mean.