Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

We study spin transport in a Hubbard chain with a strong, random, on-site potential and with spin-dependent hopping integrals $t_{\sigma }$. For the SU(2) symmetric case $t_{\uparrow }=t_{\downarrow }$, such a model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin asymmetry, $t_{\uparrow }\ne t_{\downarrow }$, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak $t_{\uparrow }\ne t_{\downarrow }$. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

Figure 1

(a) and (c) Joint probability densities $p\left(\right|J^{\perp }|,J^z)$ and $p\left(\right|J^{\perp }|,h)$, respectively, for filling $\overline{n}=N/L=0.14$. (b) Cumulative distribution functions $F^z,F^{\perp }$ compared with analytical results for the SU(2) symmetric case $F^0$ (dashed line). (d) Variance of the random field $〈h_a^2〉$ in the squeezed model as a function of disorder $W$.

Figure 2

(a) and (b) Local spin-spin correlation function $C\left(t\right)$ for fillings $\overline{n}=0.14$ and $\overline{n}=1$, respectively. Results for fixed disorder $W=4$ and various $t_{\downarrow }$ are obtained from the Lanczos method. Horizontal lines show stiffnesses $C_0$ obtained from ED for $\tilde{L}=14$. The dashed lines show the approximate power law for the SU(2) symmetric case $C\left(t\right)\propto t^{-\tilde{\lambda }/(1+\tilde{\lambda })}$. (c) Spin stiffnesses $C_0$ obtained from the Lanczos method (circles) and from ED (squares) extrapolated linearly in $1/\tilde{L}\to 0$, and (d) corresponding extrapolated values $C_0$ vs $t_{\uparrow }-t_{\downarrow }$. Error bars in (d) show uncertainty of the finite-size scaling.

Figure 3

(a) Spin stiffnesses $C_0$, as in Fig. 2 but for smaller filling $\overline{n}=0.14$. (b) corresponds to (a), but for a simplified squeezed model, while (c) and (d) refer to Fig. 2 but for a simplified model with constant $J$ (c) and uniformly distributed random $J$ (d). Note the logarithmic scales on both axes in (a) and (b).

Figure 4

$C\left(t\right)$ obtained for the original disordered Hubbard model, compared with results for the corresponding squeezed (Heisenberg) model at fixed disorder $W=8$: (a) for $\overline{n}=1/3$ and the SU(2) symmetric case, (b) for different asymmetries $t_{\downarrow }<1$, and (c) filling $\overline{n}=8/14=0.57$ closer to quarter filling. (d) Charge-charge correlation function $C^n\left(t\right)$ for the Hubbard model.