Fig. 4: Dynamics of a pumped metal in the effective theory.
a, b Evolution with time of momentum-resolved charge \({C}_{k}(t)={{{{{{{\mathcal{F}}}}}}}}\{{C}_{r}(t)\}\) (a) and spin \({S}_{k}(t)={{{{{{{\mathcal{F}}}}}}}}\{{S}_{r}(t)\}\) (b) correlation functions (\({{{{{{{\mathcal{F}}}}}}}}\) denotes the Fourier transform, \({C}_{r}\equiv \langle {\hat{n}}_{i}{\hat{n}}_{i+r}\rangle -\langle {\hat{n}}_{i}\rangle \langle {\hat{n}}_{i+r}\rangle\) and \({S}_{r}\equiv \langle ({\hat{n}}_{i,\uparrow }-{\hat{n}}_{i,\downarrow })({\hat{n}}_{i+r,\uparrow }-{\hat{n}}_{i+r,\downarrow })\rangle\)) for gq = 0.25 and ω = π/2 in the effective model given by Eqs. (4) and (5) from iTEBD simulations. c–h Dependence on time of raw (c–e) and time-averaged (f–h) double occupancy \(\langle {\hat{n}}_{i,\uparrow }{\hat{n}}_{i,\downarrow }(t)\rangle\), π-charge Cπ(t) and π-spin Sπ(t) correlations for various gq at ω = π/2 in the exact model (solid line) and the effective model is given by Eqs. (4) and (5) (dashed line) from iTEBD simulations. A bar label over an observable symbol denotes time averaging: \(\overline{\langle \hat{O}(t)\rangle }=\frac{1}{t}\int\nolimits_{0}^{t}{{{{{{{\rm{d}}}}}}}}\tau \langle \hat{O}(\tau )\rangle\). We observe good agreement between results obtained in the effective model and the exact simulations of the fully coupled model, including the rapid flattening of charge and spin correlations in the course of the dynamics.
