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arXiv:2304.02671 · Physical review. B./Physical review. B

Noise-induced universal diffusive transport in fermionic chains

Christopher M. Langlett, Shenglong Xu

Published Nov 27, 2023• 3 citations
arXivHTMLPDF

Abstract

We develop a microscopic transport theory in a randomly driven fermionic model with and without a linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of ballistic transport or Stark localization in the clean limit. The universal diffusive behavior is attributed to a noise-induced bound state arising in the operator equations of motion at small momentum. By mapping the noise-averaged operator equation of motion to a one-dimensional non-Hermitian hopping model, we analytically solve for the diffusion constant, which scales nonmonotonically with noise strength, revealing regions of enhanced and suppressed diffusion from the interplay between on-site and bond dephasing noise, and a linear potential. For large on-site dephasing, the diffusion constant vanishes, indicating an emergent localization. On the other hand, the operator equation becomes the diffusion equation for strong bond dephasing and is unaffected by additional arbitrarily strong static terms that commute with the local charge, including density-density interactions. The bound state enters a continuum of scattering states at finite noise and vanishes. However, the bound state reemerges at an exceptional-like point in the spectrum after the bound-to-scattering state transition. We then characterize the fate of Stark localization in the presence of noise.

DOI
10.1103/physrevb.108.l180303

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We develop a microscopic transport theory in a randomly driven fermionic model with and without a linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of ballistic transport or Stark localization in the clean limit. The universal diffusive behavior is attributed to a noise-induced bound state arising in the operator equations of motion at small momentum. By mapping the noise-averaged operator equation of motion to a one-dimensional non-Hermitian hopping model, we analytically solve for the diffusion constant, which scales nonmonotonically with noise strength, revealing regions of enhanced and suppressed diffusion from the interplay between on-site and bond dephasing noise, and a linear potential. For large on-site dephasing, the diffusion constant vanishes, indicating an emergent localization. On the other hand, the operator equation becomes the diffusion equation for strong bond dephasing and is unaffected by additional arbitrarily strong static terms that commute with the local charge, including density-density interactions. The bound state enters a continuum of scattering states at finite noise and vanishes. However, the bound state reemerges at an exceptional-like point in the spectrum after the bound-to-scattering state transition. We then characterize the fate of Stark localization in the presence of noise.
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.
An environment interacting with a quantum system can enhance transport through the suppression of quantum effects responsible for localization. In this paper, we study the interplay between bulk dephasing and a linear potential in a boundary-driven tight-binding chain. A linear potential induces Wannier-Stark localization in the absence of noise, while dephasing induces diffusive transport in the absence of a tilt. We derive an approximate expression for the steady-state current as a function of both dephasing and tilt which closely matches the exact solution for a wide range of parameters. From it, we find that the maximum current occurs for a dephasing rate equal to the period of Bloch oscillations in the Wannier-Stark localized system. We also find that the current displays a maximum as a function of the system size, provided that the total potential tilt across the chain remains constant. Our results can be verified in current experimental platforms and represents a step forward in analytical studies of environment-assisted transport.
We study a general one-dimensional spinless fermionic system subject to a localized source, sink, and bulk dephasing. Within the Lindblad framework, we compute the time evolution of the density profile and spatial correlation functions. We find that the presence of bulk dephasing suppresses certain coherent quantum features, such as the Friedel oscillations, and it alters the transport dynamics to exhibit two distinct dynamical regimes instead of three as observed in the absence of dephasing. This effect can be understood as the destruction of ballistic motion caused by the dephasing noise. Under strong dephasing, the density profile becomes similar to the one expected for a classical diffusive regime. We also investigate the system in the presence of both a localized source and sink, placed at a distance of ΔΔΔ. Interestingly, quantum coherence generates secondary density peaks at integer multiples of the source-sink separation ΔΔΔ, which are systematically washed out as bulk dephasing drives the system toward the classical diffusive limit.
A key insight from recent studies is that noise, such as dephasing, can improve the efficiency of quantum transport by suppressing coherent single-particle interference effects. However, it is not yet clear whether dephasing can enhance transport in an interacting many-body system. Here, we address this question by analyzing the transport properties of a boundary driven spinless fermion chain with nearest-neighbor interactions subject to bulk dephasing. The many-body nonequilibrium stationary state is determined using large-scale matrix product simulations of the corresponding quantum master equation. We find dephasing enhanced transport only in the strongly interacting regime, where it is shown to induce incoherent transitions bridging the gap between bound dark states and bands of mobile eigenstates. The generic nature of the transport enhancement is illustrated by a simple toy model, which contains the basic elements required for its emergence. Surprisingly, the effect is significant even in the linear response regime of the full system, and it is predicted to exist for any large and finite chain. The response of the system to dephasing also establishes a signature of an underlying nonequilibrium phase transition between regimes of transport degradation and enhancement. The existence of this transition is shown not to depend on the integrability of the model considered. As a result, dephasing enhanced transport is expected to persist in more realistic nonequilibrium strongly correlated systems.
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.
We study the real-time dynamics of local occupation numbers in a one-dimensional model of spinless fermions with a random on-site potential for a certain class of initial states. The latter are thermal (mixed or pure) states of the model in the presence of an additional static force but become nonequilibrium states after a sudden removal of this static force. For this class and high temperatures, we show that the induced dynamics is given by a single correlation function at equilibrium, independent of the initial expectation values being prepared close to equilibrium (by a weak static force) or far away from equilibrium (by a strong static force). Remarkably, this type of universality holds true in both the ergodic phase and the many-body localized regime. Moreover, it does not depend on the specific choice of a unit cell for the local density. We particularly discuss two important consequences. First, the long-time expectation value of the local density is uniquely determined by the fluctuations of its diagonal matrix elements in the energy eigenbasis. Thus, the validity of the eigenstate thermalization hypothesis is not only a sufficient but also a necessary condition for thermalization. Second, the real-time broadening of density profiles is always given by the current autocorrelation function at equilibrium via a generalized Einstein relation. In the context of transport, we discuss the influence of disorder for large particle-particle interactions, where normal diffusion is known to occur in the disorder-free case. Our results suggest that normal diffusion is stable against weak disorder, while they are consistent with anomalous diffusion for stronger disorder below the localization transition. Particularly, for weak disorder, Gaussian density profiles can be observed for single disorder realizations, which we demonstrate for finite lattices up to 31 sites.