Disorder enhanced transport as a general feature of long-range hopping models

TL;DR

This work investigates quantum transport in a one-dimensional disordered chain with distance-dependent long-range hopping $-\gamma/r^\alpha$. Using a Lindblad pumping/draining framework, it demonstrates that Disorder-Enhanced Transport (DET) is a universal feature for $0<\alpha\le 3$, characterized by a first onset threshold $W_1^\alpha$ and a subsequent end threshold $W_{GAP}^\alpha$ where a local current maximum occurs. The analysis introduces an effective nearest-neighbor scale $\Omega_\alpha = \gamma\left(1-2^{-\alpha}\right)$ and links the DET behavior to the tail structure of a single dominant eigenstate, with the end point connected to the energy-gap scaling via $C_\alpha$ and the spectral radius $\Delta E$. Extensions to $\alpha>1$ show DET persists up to $\alpha\approx 3$, with different regimes for the peak location depending on $\alpha$ and system size. The results provide a general framework for disorder-assisted transport in realistic long-range systems (e.g., molecular aggregates, Rydberg ensembles, and cavity-QED setups) and offer scalable analytic and numerical benchmarks for future many-body extensions.

Abstract

We analyze the interplay of disorder and long-range hopping in a paradigmatic one dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping it was shown in Chavez et al, Phys. Rev. Lett. 126, 153201 (2021), that the current can increase with disorder in the Disorder-Enhanced-Transport (DET) regime. Here, by analyzing models with variable hopping range decaying as $1/r^α$ with the distance $r$ among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit $α<1$ but even for weak long-range $1 \le α\le 3$. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long range hopping is present.

Figures (15)

• Figure 1: A disordered chain with excitation pumping $\gamma_p$ at one edge of the chain and draining $\gamma_d$ at the opposite edge. The energy of the sites is disordered. Here, $-\gamma/r^\alpha$ is the distance-dependent long-range hopping between each pair of sites.
• Figure 2: (a) Rescaled typical current $\hbar I^{typ}/\gamma$ as a function of disorder strength $W/\gamma$ for a chain of $N = 3200$ sites and several finite range interaction parameters $\alpha$. The black dashed line shows the case $\alpha = \infty$. (b) Rescaled typical current $\hbar I^{typ}/\gamma$ as a function of disorder strength $W/\gamma$ for a long-range finite interaction range $\alpha = 1/3$ and different system sizes $N$. In both the panels the error bars are given by the standard deviation of the average over the different configurations and $\gamma_p = \gamma_d = \gamma$ and $N \times N_r = 10^5$.
• Figure 3: Rescaled typical current $\hbar I^{typ}/\gamma$ as a function of the normalized disorder strength $W/W_1^\alpha$ for different system sizes $N$ and interaction parameters $\gamma$ and $\alpha$. Here, $\gamma_p=\gamma_d=1$ and $N\times N_r = 10^5$.
• Figure 4: Numerical energy gap $\Delta$ (dots) between the first excited state and the energy gap for $N = 3200$ and $W = 1$ and $W = 10^2$ as a function of the interaction strength $\gamma$. The dashed lines represent the theoretical prediction given in Eq. \ref{['deltaPF']}. The arrows indicate the interaction strength $\gamma_{cr}$ at which the energy gap opens given in Eq. (\ref{['criticalgamma']}). Here, $\alpha = 1/3, \gamma_p=\gamma_d=1$ and $N\times N_r = 10^5$.
• Figure 5: Rescaled typical current $\hbar I^{typ}/\gamma$ as a function of the normalized disorder strength $W/W_{GAP}^\alpha$ for different system sizes $N$ and interaction parameters $\gamma$ and $\alpha$. Here, $\gamma_p=\gamma_d=1$ and $N\times N_r = 10^5$.