Activating Many-Body Localization in Solids by Driving with Light

Because of the presence of phonons, many-body localization (MBL) does not occur in disordered solids, even if disorder is strong. Local conservation laws characterizing an underlying MBL phase decay due to the coupling to phonons. We show that this decay can be compensated when the system is driven out of equilibrium. The resulting variations of the local temperature provide characteristic fingerprints of an underlying MBL phase. We consider a one-dimensional disordered spin chain, which is weakly coupled to a phonon bath and weakly irradiated by white light. The irradiation has weak effects in the ergodic phase. However, if the system is in the MBL phase, irradiation induces strong temperature variations despite the coupling to phonons. Temperature variations can be used similar to an order parameter to detect MBL phases, the phase transition, and a MBL correlation length.

Figure 1

(a) Profile of local temperatures in system coupled to a phonon bath at temperature $T_p$ and driven weakly by white light. The temperature variations are large in the MBL phase (red circles), while they are vanishing in the ergodic phase (black squares). (b), (c) Fluctuations of the temperature can be used as an effective order parameter to detect a MBL transition. In the limit of vanishing coupling to the phonons and the drive, ${\epsilon }_d$, ${\epsilon }_p\to 0$, while ${\epsilon }_d/{\epsilon }_p\to \text{const}$, temperature fluctuation only arises in the MBL phase. Both a smooth transition (b) or a jump at the critical point (c) are consistent with our results obtained on small systems. Finite coupling, ${\epsilon }_d$, ${\epsilon }_p>0$, is expected to smoothen the transition into a crossover.

Figure 2

(a) Average fluctuation of local temperatures $\delta T$ normalized by the average temperature $\overline{T}$ as function of disorder strength $h$ for the system sizes $N=6$, 8, 10, 12. (b) The logarithmic plot shows that $\delta T/\overline{T}$ drops exponentially in system size in the ergodic phase, Eq. (7). The $N$ dependence for small $h$ is shown in the inset. (c) A data collapse is obtained by rescaling using $h_c=7$, $\nu =2.6$, $\beta =0$. Inset: Same scaling plot on a linear scale. Parameters: $T_p=10,U=2,({\epsilon }_d/{\epsilon }_p{)}^2=0.3$.

Figure 3

Correlation length as function of the disorder strength $h$. For small $h$ the correlation length is defined by Eq. (7), see Fig. 2. For large $h$ it is calculated from the spatial correlations of $\delta T$ discussed in Fig. 4. (Inset) The critical exponent $\nu$ can be extracted from the fit ${\xi }_e\sim [1/(h_c-h{)}^{\nu }]$. We get $\nu \approx 2.6$ assuming $h_c=7$ (see text).

Figure 4

Correlation function of the local temperature defined by $C(\delta )=⟨(T_{n,i}-\overline{T})(T_{n,i+\delta }-\overline{T})⟩$. In the MBL phase, temperature fluctuates on a rather short length scale associated with the localization length ${\xi }_l$. Parameters: $N=12$, $T_p=10,U=2,({\epsilon }_d/{\epsilon }_p{)}^2=0.3$.