Fig. 3: Dynamics of momentum-resolved electronic correlations.
We study the evolution with time of momentum-resolved charge \({C}_{k}(t)={{{{{{{\mathcal{F}}}}}}}}\{{C}_{r}(t)\}\) (a), spin \({S}_{k}(t)={{{{{{{\mathcal{F}}}}}}}}\{{S}_{r}(t)\}\) (b), and pairing \({P}_{k}(t)={{{{{{{\mathcal{F}}}}}}}}\{{P}_{r}(t)\}\) (c) correlation functions for gq = 0.25 and ω = π/2 and the dependence on time of certain k (0, π) correlations for various gq at ω = π/2 (d). Note the k-axis of the Pk(t) plot in (c) has been inverted for better visibility, and the y-axis labels of the 0/π correlations in (d) have been placed at the top of the corresponding plots. Here, \({C}_{r}\equiv \langle {\hat{n}}_{i}{\hat{n}}_{i+r}\rangle -\langle {\hat{n}}_{i}\rangle \langle {\hat{n}}_{i+r}\rangle ,{S}_{r}\equiv \langle ({\hat{n}}_{i,\uparrow }-{\hat{n}}_{i,\downarrow })({\hat{n}}_{i+r,\uparrow }-{\hat{n}}_{i+r,\downarrow })\rangle\) and \({P}_{r}\equiv \langle {c}_{i,\uparrow }^{{{{\dagger}}} }{c}_{i,\downarrow }^{{{{\dagger}}} }{c}_{i+r,\downarrow }{c}_{i+r,\uparrow }\rangle\). \({{{{{{{\mathcal{F}}}}}}}}\) denotes the Fourier transform. Charge, spin, and pairing correlations all rapidly flatten in the course of the dynamics. Note conservation of C0(t) and S0(t) in the dynamics.
