Effects of interaction symmetry on delocalization and energy transport in one-dimensional disordered lattices

We study effects of interaction symmetry in one-dimensional, momentum-conserving disordered lattices. It is found that asymmetric and symmetric interparticle interactions may result in significant difference: localized modes can be delocalized by very weak asymmetric interactions but survive much stronger symmetric interactions. Moreover, in the delocalization regime, asymmetric and symmetric interactions also have qualitatively different effects on transport: the former (the latter) may lead to a fast decaying (slow power-law decaying) heat current correlation function and in turn a convergent (divergent) heat conductivity. A method for detecting delocalization in systems at a nonzero temperature is proposed as well.

Figure 1

The amplitude of the wave passing through the lattice of size $N=512$. Panels (a) and (b) are for the DFPU-$\beta$ model and (c) is for the DFPU-$\alpha -\beta$ model. As comparison, the vertical dashed line in each panel indicates the mobility edge of the DH system.

Figure 2

The snapshot of the spatial-temporal correlation function of the energy density fluctuations for (a) the DH model, (b) the DFPU-$\beta$ model, and (c) the DFPU-$\alpha -\beta$ model at time $t=1700$. The system size is $N=4096$ and the temperature is $T={10}^{-3}$.

Figure 3

The height of the center peak in the spatial-temporal correlation function of the energy density fluctuations (see Fig. 2) as a function of time.

Figure 4

The correlation function of the energy current. (a) $T={10}^{-3}$, which is below the delocalization threshold for the DFPU-$\beta$ model; (b) $T=0.1$, delocalization occurs in both the DFPU-$\beta$ model and the DFPU-$\alpha -\beta$ model. The black dotted lines indicating scaling $\sim t^{-0.5}$ (a) and $\sim t^{-1}$ (b), respectively, are for reference.