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Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star

Jiaxiu Li, Ye Cao, and Ning Wu
Phys. Rev. B 106, 024302 – Published 5 July 2022
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  • INTRODUCTION
  • MODEL AND METHODOLOGY
  • THE NÉEL STATE |AF〉: RELAXATION OF…
  • THE GROUND STATE |GXXZ〉: GROWTH OF THE…
  • CONCLUSIONS AND DISCUSSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Interacting central spin systems, in which a central spin is coupled to a strongly correlated spin bath with intrabath interaction, consist of an important class of spin systems beyond the usual Gaudin magnet. These systems are relevant to several realistic setups and serve as an interesting platform to study interaction controlled decoherence and frustration induced instability of magnetic order. Using an equations-of-motion method based on analytical representations of spin-operator matrix elements in the XX chain, we obtain exact long-time dynamics of a generalized Heisenberg star consisting of a spin-S central spin and an inhomogeneously coupled XXZ chain of N≤16 bath spins. In contrast to previous studies where the central spin dynamics is mainly concerned, we focus on the influence of the central spin on the dynamics of magnetic orders within the spin bath. By preparing the XXZ bath in a Néel state, we find that in the gapless phase of the bath even weak system-bath coupling could lead to nearly perfect relaxation of the antiferromagnetic order. In the gapped phase, the staggered magnetization decays rapidly and approaches a steady value that increases with increasing anisotropy parameter. These findings suggest the possibility of controlling internal dynamics of strongly correlated many-spin systems by certain coupled auxiliary systems of even few degrees of freedom. We also study the dynamics of the Rényi entanglement entropy of the central spin when the bath is prepared in the ground state. Both the overall profile and initial growth rate of the Rényi entropy are found to exhibit minima at the critical point of the XXZ bath.

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    • Received 18 August 2021
    • Revised 20 April 2022
    • Accepted 29 June 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.024302

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Open quantum systems & decoherenceSpin dynamics
    1. Physical Systems
    Quantum spin models
    1. Techniques
    Heisenberg model
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Jiaxiu Li1,2, Ye Cao2, and Ning Wu1,2,*

    • 1Center for Quantum Technology Research, School of Physics, Beijing Institute of Technology, Beijing 100081, China
    • 2Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China

    • *wunwyz@gmail.com

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    Issue

    Vol. 106, Iss. 2 — 1 July 2022

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    Images

    • Figure 1
      Figure 1

      An inhomogeneous Heisenberg star consists of a spin-S central spin and a spin bath modeled by an XXZ ring, with the two part interacting via inhomogeneous XXZ-type hyperfine coupling.

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    • Figure 2
      Figure 2

      Structure of the block Hamiltonian HI,α for a fixed α with −S≤α≤S. The main diagonal blocks are associated with the spin-operator matrix elements Gχ⃗n,χ⃗n′({gj′}) and G¯χ⃗n,χ⃗n′ (with red sides), while the off-diagonal blocks are associated with the matrix elements Fη⃗n+1,χ⃗n({gj}) (with dotted green sides). The blue line indicates the diagonal terms.

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    • Figure 3
      Figure 3

      Dynamics of the staggered magnetization 〈ms(t)〉 in the pure XXZ chain (gj=gj′=0,∀j) with N=14 (thin curves) and 16 (thick curves) sites. The initial state is chosen as the Néel state |AF〉=|↓↑⋯↓↑〉. The time evolution up to Jt=4 is independent of N and expected to match the thermodynamic limit result.

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    • Figure 4
      Figure 4

      Time evolution of the staggered magnetization 〈ms(t)〉 in a generalized Heisenberg star composed of a S=1/2 central spin and an XXZ chain with N=16 sites. The XXZ bath is prepared in the Néel state |AF〉=|↓↑⋯↓↑〉 and the initial state of the central spin is |ϕ(S)〉=12(|↑〉+|↓〉). The corresponding dynamics of the central spin decoherence factor |r(t)|=|〈S+(t)/〈S+(0)〉| is shown in the right upper corners of (b), (c), and (d). Other parameters: Λ=1 and ω=λ=0.

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    • Figure 5
      Figure 5

      Time evolution of the staggered magnetization 〈ms(t)〉 in a Heisenberg star composed of a single S=1/2 central spin and an isotropic XXZ chain with N=16 sites and J′/J=1. The inset shows the dynamics up to an intermediate time ωfluct=100. Note that we use ωfluc as an overall energy scale so that the initial decay of 〈ms(t)〉 is accelerated by increasing the intrabath coupling J/ωfluc. Other parameters: Λ=1 and ω=λ=0.

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    • Figure 6
      Figure 6

      Time evolution of the staggered magnetization 〈ms(t)〉 in a Heisenberg star composed of an isotropic XXZ chain with N=14 and a central spin with S=1/2, 1, 3/2, and 2. The intrabath coupling is chosen to be J/ωfluc=0.1 (strong system-bath coupling) and the results for several values of the anisotropy parameter J′/J are presented. Other parameters: Λ=1 and ω=λ=0.

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    • Figure 7
      Figure 7

      Dynamics of the Rényi entanglement entropy R2(t) of a spin-1 central spin coupled to an XXZ chain with N=14 sites. The bath is prepared in the ground state |ϕ(B)〉=|GXXZ〉 for fixed J′/J and the intrabath coupling is chosen as J/ωfluc=0.1 (strong system-bath coupling). The central spin is prepared in an equally weighted superposition state |ϕ(S)〉=13(|1〉+|0〉+|−1〉). The left inset shows the short-time dynamics of R2(t) up to ωfluct=1.5 and the right inset shows the growth rate γ [see Eq. (33)] as a function of J′/J. Other parameters: Λ=1 and ω=λ=0.

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