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arXiv:2406.00768 · Physical review. B./Physical review. B

Anomalous transport in long-ranged open quantum systems

Abhinav Dhawan, Katha Ganguly, Manas Kulkarni, Bijay Kumar Agarwalla

Published Aug 9, 2024• 12 citations
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Abstract

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.

DOI
10.1103/physrevb.110.l081403

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We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent \ensuremathα\ensuremath{\alpha}\ensuremathα. 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<\ensuremathα<1.51<\ensuremath{\alpha}<1.51<\ensuremathα<1.5, and for \ensuremathα>1.5\ensuremath{\alpha}>1.5\ensuremathα>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.
The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with nearest-neighbor and beyond, i.e., long-ranged (power-law) hopping, and (ii) a lattice that is interacting via short-range interactions modeled by a fermionic quartic Hamiltonian. We study the evolution of the local density profile ni(t)n_i(t)ni​(t) within the system and the growth of the total particle number N(t)N(t)N(t) in it. For case (i), we provide analytical insights into the dynamics of the nearest-neighbor model using an adiabatic approximation, which relies on assuming faster relaxation of coherences of the single particle density matrix. For case (ii), we perform numerical computations using the time-evolving block decimation (TEBD) algorithm and analyze the density profile and the growth exponent in N(t)N(t)N(t). Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems, such as local source and bulk dephasing. It brings out rich dynamics, including universal dynamical scaling and anomalous behavior across various time scales and is of relevance to various quantum simulation platforms.
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.
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.
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.
We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing subdiffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e., in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known nonequilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the subdiffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing subdiffusive scaling of conductance with system size in a two-terminal setup are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.
We study nonequilibrium steady-state transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-Hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.