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arXiv:2610.33393

Controlling transport with structured long-range hopping

Boris Gurevich, Michael H. Kolodrubetz

cond-mat.dis-nnquant-phSubmitted Oct 24, 2026• Announced Oct 27, 2026• 0 citations
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Abstract

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.

AI Summary

The paper asks how the spatial profile of cavity-mediated, long-range hopping changes localization and disorder-enhanced transport in a one-dimensional Anderson chain. It studies nearest-neighbor hopping supplemented by a rank-one term $H_L=-\gamma\sum_{ij}\eta_i\eta_j|i\rangle\langle j|$, comparing uniform, random, and sinusoidal coupling profiles. For uniform $\eta_j$, a weak-to-moderate-disorder regime has strongly suppressed eigenstate spatial variance; the previously observed disorder-enhanced transport regime is interpreted as recovery from this suppression. Random amplitudes, especially zero-mean $\eta_j\in[-1,1]$, largely remove the suppression, whereas sinusoidal profiles retain it. The explanation uses an exact rank-one secular equation in the Anderson eigenbasis: uniform and sinusoidal profiles concentrate coupling weight on selected low-disorder momentum states, suppressing mixing among other Anderson orbitals. Random profiles distribute that weight more broadly. Neglecting interference and statistically factorizing orbital-mixing weights from spatial profiles gives $\langle\sigma_T^2\rangle\simeq P_A\langle\sigma_A^2\rangle+(1-P_A)N^2/24$, where $P_A$ is the full eigenstates’ inverse participation ratio in the Anderson basis. Numerical comparisons use chains of $N=1000$–$3000$, generally nine disorder realizations. Single-excitation drain-transfer calculations, averaged over 100 realizations, show corresponding qualitative transport trends. The variance approximation fails at very weak disorder for nonuniform profiles, where interference matters. An explicit analytical disorder dependence of $P_A$ remains unavailable. Transport is estimated from transient transfer times rather than a full pumped steady state. Experimental implementation, accompanying nearest-neighbor hopping disorder, and many-excitation dynamics remain open extensions.

Little sign of AI-generated textIncrementalStrong assumptions

Error found: The weak-disorder level-spacing argument neglects the clean ring’s ±k degeneracies, whose generic first-order disorder splitting scales as W/√N rather than the asserted W, undermining the quantitative condition inferred from that estimate. The general-observable expression and appendix transpose the eigenvector coefficients relative to their definition, although correcting these indices leaves the final statistically factorized formulas unchanged.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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15 pages, 7 figures

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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.
The paper asks how the spatial profile of cavity-mediated, long-range hopping changes localization and disorder-enhanced transport in a one-dimensional Anderson chain. It studies nearest-neighbor hopping supplemented by a rank-one term HL=−γ∑ijηiηj∣i⟩⟨j∣H_L=-\gamma\sum_{ij}\eta_i\eta_j|i\rangle\langle j|HL​=−γ∑ij​ηi​ηj​∣i⟩⟨j∣, comparing uniform, random, and sinusoidal coupling profiles.
For uniform ηj\eta_jηj​, a weak-to-moderate-disorder regime has strongly suppressed eigenstate spatial variance; the previously observed disorder-enhanced transport regime is interpreted as recovery from this suppression. Random amplitudes, especially zero-mean ηj∈[−1,1]\eta_j\in[-1,1]ηj​∈[−1,1], largely remove the suppression, whereas sinusoidal profiles retain it. The explanation uses an exact rank-one secular equation in the Anderson eigenbasis: uniform and sinusoidal profiles concentrate coupling weight on selected low-disorder momentum states, suppressing mixing among other Anderson orbitals. Random profiles distribute that weight more broadly.
Neglecting interference and statistically factorizing orbital-mixing weights from spatial profiles gives ⟨σT2⟩≃PA⟨σA2⟩+(1−PA)N2/24\langle\sigma_T^2\rangle\simeq P_A\langle\sigma_A^2\rangle+(1-P_A)N^2/24⟨σT2​⟩≃PA​⟨σA2​⟩+(1−PA​)N2/24, where PAP_APA​ is the full eigenstates’ inverse participation ratio in the Anderson basis. Numerical comparisons use chains of N=1000N=1000N=1000–300030003000, generally nine disorder realizations. Single-excitation drain-transfer calculations, averaged over 100 realizations, show corresponding qualitative transport trends.
The variance approximation fails at very weak disorder for nonuniform profiles, where interference matters. An explicit analytical disorder dependence of PAP_APA​ remains unavailable. Transport is estimated from transient transfer times rather than a full pumped steady state. Experimental implementation, accompanying nearest-neighbor hopping disorder, and many-excitation dynamics remain open extensions.
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.
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.
It has become widely accepted that particles with long-range hopping do not undergo Anderson localization. However, several recent studies demonstrated localization of particles with long-range hopping. In particular, it was recently shown that the effect of long-range hopping in one-dimensional (1D) lattices can be mitigated by cooperative shielding, which makes the system behave effectively as one with short-range hopping. Here, we show that cooperative shielding, demonstrated previously for 1D lattices, extends to 3D lattices with isotropic long-range ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ hopping, but not to 3D cubic lattices with anisotropic long-range hopping. The specific anisotropy we consider corresponds to the interaction between dipoles aligned along one of the principal axes of the lattice. We demonstrate the presence of localization in 3D lattices with uniform ($\ensuremath{\alpha}=0$) isotropic long-range hopping and the absence of localization with uniform anisotropic long-range hopping by using the scaling behavior of eigenstate participation ratios. We use the scaling behavior of participation ratios and energy-level statistics to show that the existence of delocalized, extended nonergodic, or localized states in the presence of disorder depends on both the exponents $\ensuremath{\alpha}$ and the anisotropy of the long-range hopping amplitudes.
Environmental noise can enhance transport, an effect known as environmental noise-assisted quantum transport. Most theoretical studies focus on optimizing system parameters under spatially uniform system-environment coupling. Here, instead, we optimize the environmental noise itself by allowing for site-dependent dephasing. We investigate steady-state transport in one-dimensional lattices with either ramped or disordered energy landscapes, considering both short- and long-range coherent tunneling. In the absence of environmental effects, in the thermodynamic limit these systems can exhibit localization, and thus suppressed transport, arising from destructive interference. Using a Lindblad master equation framework, we implement local dephasing optimized to maximize steady-state population flux. We find that for ramp potentials, short-range tunneling favors selective dephasing on alternating sites, whereas long-range tunneling benefits from a dephasing profile that increases with distance from the injection site. In energetically disordered systems, strongly detuned sites require enhanced local dephasing under short-range tunneling to facilitate transport. In all cases, we find that site-optimized dephasing allows higher transport efficiency than uniform dephasing, and it is accompanied by increased spatial delocalization of the steady state. Our results provide microscopic insight into the interplay between coherent dynamics and environmental noise. Dephasing broadens energy levels locally, helping to overcome detuning and destructive interference. More generally, we establish spatially-structured environmental noise as a strategy for controlling both quantum transport and state coherence in open systems.
A different type of system with coupled ordered-disordered chains has given rise to considerable interest recently, as it has a variety of applications in nanostructures and biological systems such as DNA molecules. We investigate the localization/delocalization of coupled one-dimensional systems composed of one disordered chain (chain I) and another ordered chain (chain II), focusing on the interplay among the disorder, correlation, and interchain coupling. We find that for systems where chain I exhibits uncorrelated disorder, charge transport in chain I (II) is enhanced (suppressed), as the disorder in chain I leads to the localization of all states in both chains. However, for chain I with hopping amplitude t1{t}_{1}t1​ and long-range correlated disorder (with power-law spectral density and disorder strength WWW), we find there is a localization/delocalization transition for the case $W\ensuremath{\le}4{t}_{1}$, induced by interchain coupling. For W>4t1W>4{t}_{1}W>4t1​, we find there is a quantum-phase transition at finite interchain coupling Vc{V}_{c}Vc​: The interchain coupling induces appearance of two channels of extended states for V>VcV>{V}_{c}V>Vc​ while there is only one channel of extended states for V<VcV<{V}_{c}V<Vc​.
We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S(t)\ensuremath{\sim}lnt$ and the saturated entanglement entropy scales with system size LLL as $S(L,t\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}lnL$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.