Locality Bound for Dissipative Quantum Transport

Abstract

We prove an upper bound on the diffusivity of a general local and translation invariant quantum Markovian spin system: $D\le D_0+\left(\alpha v_{\text{LR}}\tau +\beta \xi \right)v_{\text{C}}$. Here $v_{\text{LR}}$ is the Lieb-Robinson velocity, $v_{\text{C}}$ is a velocity defined by the current operator, $\tau$ is the decoherence time, $\xi$ is the range of interactions, $D_0$ is a microscopically determined diffusivity and $\alpha$ and $\beta$ are precisely defined dimensionless coefficients. The bound constrains quantum transport by quantities that can either be obtained from the microscopic interactions ($D_0,v_{\text{LR}},v_{\text{C}},\xi$) or else determined from independent local non-transport measurements ($\tau ,\alpha ,\beta$). We illustrate the general result with the case of a spin half XXZ chain with on-site dephasing. Our result generalizes the Lieb-Robinson bound to constrain the sub-ballistic diffusion of conserved densities in a dissipative setting.

arXiv comment5 pages, 1 figure, revised for PRL

References in corpus (32)

• Spintronics: Fundamentals and applications
• The density-matrix renormalization group in the age of matrix product states
• Graphene Spintronics
• Black holes and the butterfly effect
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Localized shocks
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Saturation of electrical resistivity
• Theory of universal incoherent metallic transport
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Universality of the Mott-Ioffe-Regel limit in metals
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Lieb-Robinson and the butterfly effect
• Spin diffusion from an inhomogeneous quench in an integrable system
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Scrambling and thermalization in a diffusive quantum many-body system
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Relaxation times of dissipative many-body quantum systems
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Quantum transport in ultracold atoms
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Quantum dynamics of thermalizing systems
• Influence of dephasing on many-body localization
• Universal spin dynamics in two-dimensional Fermi gases
• An upper bound on transport
• Dephasing-induced diffusive transport in anisotropic Heisenberg model
• Quantum thermalization dynamics with Matrix-Product States
• Heat transport in the $XXZ$ spin chain: from ballistic to diffusive regimes and dephasing enhancement
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
• Lower bounds on high-temperature diffusion constants from quadratically extensive almost conserved operators
• Local approximation of observables and commutator bounds

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• Operator size at finite temperature and Planckian bounds on quantum dynamics
• Nonequilibrium steady-state Kubo formula: equality of transport coefficients
• Planckian properties of 2D semiconductor systems
• A Bound on Thermalization from Diffusive Fluctuations
• Quantum stochastic transport along chains
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