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

Abstract

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 composite system consisting of a spin-S central spin and an XXZ chain, with the two interacting via inhomogeneous XXZ-type hyperfine coupling. Three types of initial bath states, namely, the Néel state, the ground state, and the spin coherent state are considered. We study the reduced dynamics of both the central spin and the XXZ bath. For the Néel state, we find that strong hyperfine couplings slow down the initial decay but facilitate the long-time relaxation of the antiferromagnetic order. Moreover, for fixed hyperfine coupling a larger S leads to a faster initial decay of the antiferromagnetic order. We then study the purity dynamics of an S = 1 central spin coupled to an XXZ chain prepared in the ground state. The time-dependent purity is found to reach the highest values at the critical point. We finally study the polarization dynamics of the central spin homogeneously coupled to a bath prepared in the spin coherent state. Under the resonant condition, the polarization dynamics for S > 1 2 exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to the anisotropic intrabath coupling.

Ground-state and dynamical properties of a spin-S Heisenberg star

“…We reveal the influence of central-spin size, the central-spin initial state, and the system-bath coupling strength on the staggered magnetization dynamics. Some of the observed dynamical behaviors are consistent with those obtained in an inhomogeneous Heisenberg star [12]. For example, increasing the size of the central spin and adopting a superposed central-spin initial state can both accelerate the initial decay of the antiferromagnetic order, while these effects become less prominent in the strong intrabath coupling regime.…”

“…does not change the foregoing property, as has already been observed in the investigation of the central spin coherence from a pure state [13]. Thus, to obtain nontrivial dynamics of the central spin induced by the intrabath coupling, one has to either include the thermal effect [13] or to go beyond the homogeneous systembath coupling or isotropic intrabath coupling [12]. In spite of these facts, the dynamics of any bath operator η B depends on both J and g since generally [H b , η B ] ≠ 0 and S L,…”

“…Alternatively, the Heisenberg star can also be viewed as a central spin system in the presence of nearest-neighbor intrabath interactions. Recently, the solvability and real-time dynamics of higher-spin central spin models with/without intrabath interaction are studied and a richer variety of physical properties are observed compared to the spin-1/2 counterpart [11,12].…”

Ground-state and dynamical properties of a spin-$S$ Heisenberg star

“…Alternatively, the Heisenberg star can also be viewed as a central spin system in the presence of nearestneighbor intrabath interactions. Recently, the solvability and real-time dynamics of higher-spin central spin models with/without intrabath interaction are studied and a richer variety of physical properties are observed compared to the spin-1/2 counterpart [11,12].…”

“…Therefore, the dynamics generated by H is independent of the value of J at the isotropic point J = J ′ , where JH b commutes with the Hamiltonian H. For arbitrary S < N/2, the central spin dynamics simulated by using an equations-of-motion method based on analytical expressions of spin-operator matrix elements for the XX chain [22], see Ref. [12] for details of the method. The top panel of Fig.…”