Impact of dephasing on nonequilibrium steady-state transport in fermionic chains with long-range hopping

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 $1/r^{\alpha }$), where $\alpha >1$. We demonstrate the emergence of distinct transport regimes as the long-range hopping parameter, $\alpha$, is tuned. In the short-range limit ($\alpha \gg 1$), transport is diffusive. Conversely, in the long-range limit $[\alpha \sim O(1\left)\right]$, 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, ${\alpha }_c\approx 1.5$, 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.