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arXiv:2310.01323 · Physical review. B./Physical review. B

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

Subhajit Sarkar, Bijay Kumar Agarwalla, Devendra Singh Bhakuni

Published Apr 3, 2024• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.165408

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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\ensuremathα1/{r}^{\ensuremath{\alpha}}1/r\ensuremathα), where \ensuremathα>1\ensuremath{\alpha}>1\ensuremathα>1. We demonstrate the emergence of distinct transport regimes as the long-range hopping parameter, \ensuremathα\ensuremath{\alpha}\ensuremathα, is tuned. In the short-range limit (\ensuremathα\ensuremath≫1\ensuremath{\alpha}\ensuremath{\gg}1\ensuremathα\ensuremath≫1), transport is diffusive. Conversely, in the long-range limit [\ensuremathα\ensuremath∼O(1)][\ensuremath{\alpha}\ensuremath{\sim}\mathcal{O}(1)][\ensuremathα\ensuremath∼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, \ensuremathαc\ensuremath≈1.5{\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5\ensuremathαc​\ensuremath≈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.
We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.
We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. The spin–spin correlation function, on the other hand, has long-range correlations which, though, decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.
Abstract We investigate how long-range power-law hopping interaction, ∼ 1/r a , affects the characteristics of dissipative quantum transport in a nonequilibrium setting. The model under consideration is a noninteracting bosonic chain subject to thermal baths of differing temperature at its boundaries and dephasing noise which is applied uniformly to all the sites. It is shown that the steady-state current may vary nonmonotonically and has a peak for a finite a depending on the position of the cold bath. This site-specific behaviour stems back to the interference effect caused by the parity of the total sites N and the baths positions. The fractional nature of the system, along with the interplay between coherent and incoherent transport, will affect the steady state current that characterizes the transport.
In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.
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 study a recently discussed XX spin chain with nonlocal dephasing [Y.-P. Wang et al., arXiv:2310.03069] in a steady-state boundary-driven setting, confirming superdiffusive magnetization transport in the thermodynamic limit. The emergence of superdiffusion is rather interesting as the Lindblad operators causing it are a coherent sum of two terms, each of which would separately cause diffusion. One therefore has a quantum phenomenon where a coherent sum of two diffusive terms results in superdiffusion. We also study perturbations of the superdiffusive model, finding that breaking the exact form of dissipators, as well as adding interactions to the XX chain, results in superdiffusion changing into diffusion.