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  • Letter

Spin diffusion in a perturbed isotropic Heisenberg spin chain

S. Nandy, Z. Lenarčič, E. Ilievski, M. Mierzejewski, J. Herbrych, and P. Prelovšek
Phys. Rev. B 108, L081115 – Published 21 August 2023
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    Abstract

    The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization m≠0, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant D0(Δ) on the spin anisotropy Δ, with a pronounced maximum at Δ=1. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at Δ=1 that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.

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    • Received 19 December 2022
    • Revised 24 April 2023
    • Accepted 7 August 2023

    DOI:https://doi.org/10.1103/PhysRevB.108.L081115

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Ballistic transportDiffusionDissipative dynamicsMagnonsQuantum transportSpin dynamics
    1. Physical Systems
    1-dimensional spin chainsNonequilibrium systemsQuantum many-body systemsQuantum spin modelsStrongly correlated systems
    1. Techniques
    Exact solutions for many-body systemsIntegrable systemsLattice models in condensed matterLindblad equationMany-body techniquesTensor network methods
    Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

    Authors & Affiliations

    S. Nandy1, Z. Lenarčič1, E. Ilievski2, M. Mierzejewski3, J. Herbrych3, and P. Prelovšek1

    • 1Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
    • 2Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
    • 3Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland

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    Issue

    Vol. 108, Iss. 8 — 15 August 2023

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    Images

    • Figure 1
      Figure 1

      Diffusion constant D0 vs anisotropy Δ at fixed magnetization density m=1/4 for HI′ perturbation at strength g=0.3, as obtained for different system sizes via ED (L=24) and MCLM (L=28–36). (b) D0 vs Δ for isotropic (full lines) and anisotropic (dashed lines) g=0.15–0.3, obtained via MCLM for L=36. (c), (d) Integrated optical conductivity I(ω) for (c) Δ=1 and (d) Δ=1.1 as the function of the rescaled frequencies by the square of the perturbation strength ω/g2. Dashed (solid) line depicts L=20 (L=36) ED (MCLM) data.

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    • Figure 2
      Figure 2

      Diffusion constant D0 vs anisotropy Δ, as calculated via MCLM in ensembles with magnetization densities m=[0,6]/28 and g=0.2 for HI′ (main panel) and HII′ (left inset) perturbation, respectively. Right inset: Comparison of canonical m=0 and grand canonical results.

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    • Figure 3
      Figure 3

      (a) Scaling of NESS diffusion constant vs L for HI′ perturbation at various perturbation strengths g=0.15–0.4, including the unperturbed result g=0, fitted with the power laws D0∝Lζ with different ζ=[0.24–0.5]. In the inset, fitted ζ for different g are shown for Δ=1.0 and Δ=0.9. (b) Diffusion constant D0 vs Δ for HI′ perturbation of different strength g=0.15–0.4, obtained via NESS method for sizes L=30,60.

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    • Figure 4
      Figure 4

      (a) Normalized spin stiffness D* vs magnetization density m obtained from (i) extrapolated L→∞ ED data [39] (solid black points), (ii) tDMRG result Ref. [43] (open black points), and (iii) GHD exact calculation (orange line). Simple linear relation D*=2|m| (green solid line) at large magnetization and D*(m)=6.19m2ln(1/|m|) (green dashed line) at small magnetization is also presented.

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