Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

Gong Long-Yan^{1, 2, 3, †}, Ding You-Gen², Deng Yong-Qiang²

(color online) For the deterministic nearest neighbor tight binding models with exact mobility edges, (a) ΔU², (b) ΔV², (c) U_r, (d) LB, and (e) IPR as functions of eigenenergies E_β, respectively. Here, λ = −0.9t and ; the vertical dashed line is for the function E_β = E_c = t/3; the horizontal dashed line in panel (c) is for U_r = 0; lattice sizes d = 987, 2584, and 10946, respectively.