Locality Bound for Dissipative Quantum Transport

Journal Article · 22 October 2018 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.121.170601 · OSTI ID:1612850

Han, Xizhi ^[1]; Hartnoll, Sean A. ^[2]

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1. Stanford Univ., CA (United States); DOE/OSTI
2. Stanford Univ., CA (United States)

We prove an upper bound on the diffusivity of a dissipative, local, and translation invariant quantum Markovian spin system: D ≤ D₀ + (αv_LRτ + βξ)v_C. Here vLR is the Lieb-Robinson velocity, vC is a velocity defined by the current operator, τ is the decoherence time, ξ is the range of interactions, D0 is a decoherence-induced microscopic diffusivity, and α and β are precisely defined dimensionless coefficients. The bound constrains quantum transport by quantities that can either be obtained from the microscopic interactions (D₀, v_LR, v_C, ξ) or else determined from independent local nontransport measurements (τ, α, β). We illustrate the general result with the case of a spin-half XXZ chain with on-site dephasing. Furthermore, our result generalizes the Lieb-Robinson bound to constrain the sub-ballistic diffusion of conserved densities in a dissipative setting.

• Research Organization: Stanford Univ., CA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0018134
• OSTI ID: 1612850
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 17 Vol. 121; ISSN 0031-9007
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English