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arXiv:2405.20813

Unusual Diffusivity in Strongly Disordered Quantum Lattices: Random Dimer Model

Ilia Tutunnikov, Jianshu Cao

Published May 31, 2024• 1 citation
arXivHTMLPDF

Abstract

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 $t^{-1/2}$, is inversely proportional to the disorder strength, and maintains a constant frequency with an initial phase shift of $π/4$. The first peak exhibits a universal scaling of $σ^{-1}$ 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.

DOI
10.48550/arxiv.2405.20813

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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.
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.
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