Absence of full many-body localization in the disordered Hubbard chain

We present numerical results within the one-dimensional disordered Hubbard model for several characteristic indicators of the many-body localization (MBL). Considering traditionally studied charge disorder (i.e., the same disorder strength for both spin orientations) we find that even at strong disorder all signatures consistently show that while charge degree of freedom is nonergodic, the spin is delocalized and ergodic. This indicates the absence of the full MBL in the model that has been simulated in recent cold-atom experiments. Full localization can be restored if spin-dependent disorder is used instead.

Figure 1

Charge and spin imbalance correlations $C\left(\tau \right)$ and $S\left(\tau \right)$, respectively, as evaluated by the MCLM at half-filling $\overline{n}=1$ and $U=4$, at fixed system size $L=14$. The potential disorder is varied in the range $W=2–15$.

Figure 2

$C\left(\tau \right)$ and $S\left(\tau \right)$ calculated for half-filling $\overline{n}=1$ and $L=12$, for fixed disorder $W=6$ and various interaction strengths $U=0–8$.

Figure 3

Decay of the local charge and spin correlations for $U=1$ and $W=16$. (a) For the charge disorder, spin is delocalized (the red dashed curve). (b) For the independent disorder for each spin, the charge and the spin are both localized (note the two, the red and the blue curves, almost completely overlapping). The averaging involves over 400 product initial states, $L=64$.

Figure 4

Charge and spin dynamical conductivity ${\sigma }_c\left(\omega \right)$ and ${\sigma }_s\left(\omega \right)$, respectively, evaluated at half-filling $\overline{n}=1, U=4$ at fixed size $L=14$, but for various disorders $W=3–20$.

Figure 5

Average von Neumann entropy $S_2\left(t\right)$ for $U=1$ and $W=16$ in a log-log plot. Inset: semilogarithmic plot of the same data (red curve). For charge disorder (red curve) $S_2\left(t\right)$ is consistent with a power law, while for an independent disorder (blue curve in the inset) with a logarithmic growth. The same dataset as in Fig. 3, statistical fluctuations are of the size of curves thickness.