Many-body localization in system with a completely delocalized single-particle spectrum

Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessarily rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term, a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiment is proposed.

Figure 1

A schematic of the model considered in this work. The lower portion of the figure shows a random configuration of particles. The red (dark) particles are doublons, and the orange (light) particles are singlons. The upper portion of the figure is a cartoon of the charge distribution, with localized doublons and delocalized singlons.

Figure 2

Charge excitation dynamics of the random interaction Fermi-Hubbard model (1) with and without singlons in the initial state. The left panels display contour plots of the correlation function $C_i\left(t\right)$ as a function of space and time. The solid white line corresponds to the contour line, $C_i\left(t\right)=7.5\times {10}^{-3}$, and the dashed white lines highlight ballistic jets of singlons. The top right panel presents the width of the excitation as a function of time on a log-log plot, and the bottom right panel the entanglement entropy $S$ as a function of time on a semilog plot. The data have been obtained using tDMRG for $L=20$ and $\mathrm{\Delta }U=30$, and averaged over a minimum of 300 realizations.

Figure 3

Left: Excitation profile $C_i\left(t\right)$ for the initial (solid black line) and final times (gray, and dashed black lines). Right: Charge excitation width as a function of time for disordered (orange, gray lines) and clean Hubbard models (black dashed line) on a log-log plot. The parameters used for the disordered case are $-30\le U_i\le 0$, and for the clean case $U_i=-30$.

Figure 4

Same as Fig. 2 but with interaction term of Eq. (4). The data have been obtained using ED for $L=11$ and $\mathrm{\Delta }U=30$, and averaged over at least 300 realizations. Note that the simulation time was $t=1000$ for initial conditions with singlons, and $t=100$ for the initial conditions without singlons.