Delocalization of Weakly Interacting Bosons in a 1D Quasiperiodic Potential

We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger coupling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.

Figure 1

The critical coupling strength $U_c$ versus temperature obtained by directly using Eqs. (14)–(16) and the one-particle spectrum computed by exact diagonalization, for $\kappa$ close to $1/8$, $V=2.05J$, and the filling factor $\nu =1,2,4$. At $T=0$ we recover universality in $\nu U_{c0}$. The dashed line is the $T\to \infty$ asymptotics. The inset shows the spectrum on the length scale of $\zeta$ (the number of states is $\zeta \approx 40$).

Figure 2

The same as in Fig. 1 for $V=2.3J$ ($\zeta \approx 7$). In (a) $\kappa \approx 0.24$, and in (b) $\kappa$ is equal to the golden ratio. The inset in (a) shows $\nu U_c(T)$ for $\kappa \approx 1/8$ and $V=2.25J$ ($\zeta \approx 8$).