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arXiv:2601.07787

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

Elisa Zanardini, Giuseppe Luca Celardo, Nahum C. Chávez, Fausto Borgonovi

quant-phSubmitted Jan 12, 2026• Announced Jan 13, 2026• 0 citations
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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.

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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/rα1/r^α1/rα with the distance rrr 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<1α<1α<1 but even for weak long-range 1≤α≤31 \le α\le 31≤α≤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.
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/rα 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 < α < 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.
The combined effects of disorder and long-range hopping play an important role in determining localization and transport in low-dimensional quantum systems. We study transport in a one-dimensional disordered chain with nearest-neighbor hopping supplemented by a long-range hopping term. The long-range coupling is characterized by site-dependent amplitudes that may be either uniform or random. We investigate the interplay between diagonal disorder and long-range hopping, characterizing the resulting transport efficiency. We find that nearest-neighbor hopping in the presence of uniform long-range hopping amplitudes strongly suppresses delocalization over a range of weak disorder. The disorder-enhanced transport regime, established in previous studies, can be understood here as the recovery of delocalization from this strongly suppressed regime. An analytical solution in the Anderson eigenstate basis reveals the microscopic origin of this behavior. In particular, we show that the low-disorder regime of strongly suppressed delocalization can be eliminated by introducing randomness into the long-range hopping amplitudes, providing an additional mechanism for enhancing transport and qualitatively changing the response of the system to disorder.
Quantum transport in nonequilibrium settings plays a fundamental role in understanding the properties of systems ranging from quantum devices to biological systems. Dephasing---a key aspect of out-of-equilibrium systems---arises from interactions with a noisy environment and can profoundly modify transport properties. Here we investigate the impact of dephasing on the nonequilibrium steady-state transport properties of noninteracting fermions on a one-dimensional lattice with long-range hopping (proportional to $1/{r}^{\ensuremath{\alpha}}$), where $\ensuremath{\alpha}>1$. We demonstrate the emergence of distinct transport regimes as the long-range hopping parameter, $\ensuremath{\alpha}$, is tuned. In the short-range limit ($\ensuremath{\alpha}\ensuremath{\gg}1$), transport is diffusive. Conversely, in the long-range limit $[\ensuremath{\alpha}\ensuremath{\sim}\mathcal{O}(1)]$, we observe a superdiffusive transport regime. Using numerical simulations of the Lindblad master equation and corroborating these with an analysis of the current-operator norm, we identify a critical long-range hopping parameter, ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5$, below which superdiffusive transport becomes pronounced and rapidly becomes independent of the dephasing strength. Our results elucidate the intricate balance between dephasing and unitary dynamics, revealing steady-state transport features.
Using a numerically exact technique we study spin transport and entanglement growth in the delocalized phase of a disordered spin chain with long-range interactions, decaying as a power law, ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ with distance. For all considered $\ensuremath{\alpha}$'s and disorder strengths we find that the entanglement entropy grows sublinearly, and the underlying transport is subdiffusive. Since rare-blocking regions, which are central to the Griffiths theory of transport in disordered interacting systems, can be easily circumvented by long-range hops across the lattice, they cannot explain the mechanism of slow transport in long-range systems. Specifically, we show that for long-range systems the Griffiths theory predicts diffusive transport, which is inconsistent with our results.
Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum lattices. Initially, our statistical analysis of localized eigenstates reveals a distinct transition between weak and strong disorder regimes, suggesting a random distribution of dimers in highly disordered systems. Subsequently, the random dimer model predicts an oscillating diffusivity that decays as t−1/2t^{-1/2}t−1/2, is inversely proportional to the disorder strength, and maintains a constant frequency with an initial phase shift of π/4π/4π/4. The first peak exhibits a universal scaling of σ−1σ^{-1}σ−1 both in peak time and amplitude. Finally, we find that stochastic noise suppresses these oscillations and induces hopping between localized eigenstates, resulting in constant diffusion over long times. Our predictions challenge the conventional understanding of incoherent hopping under strong disorder. This offers new insights to optimize disordered systems for optoelectrical and quantum information technologies.
We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite-range hopping coupling (independent of the position). Due to long-range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited-state subspace is shielded from long-range hopping, namely it occurs as if long-range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale that diverges with the system size. We named this effect cooperative shielding. We also discuss the consequences of our findings on Anderson localization. Long-range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long-range coupling. A brief discussion on the extension of our results to generic power-law decaying long-range hopping is also given. Our preliminary results confirm that the effects found for the infinite-range case are generic.