Coherence of an extended central spin model with a coupled spin bath

Lu, Pengcheng; Shi, Hailong; Cao, Li-Ke; Wang, Xiaohui; Yang, Tao; Cao, Junpeng; Yang, Wen-Li

doi:10.1103/physrevb.101.184307

Cited by 7 publications

(11 citation statements)

References 41 publications

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“…We are also interested in the real-time dynamics of the Heisenberg star. As observed in [13], for a star prepared in a pure state, the dynamics of any observable belonging to the central spin do not depend on the intrabath coupling, and hence are equivalent to the result for a noninteracting bath. Rather than focusing on the central spin dynamics, we study the staggered magnetization dynamics within the XXX bath when it is prepared in the Néel state.…”

Section: Introductionmentioning

confidence: 70%

“…In this work, we extend the spin-1/2 Heisenberg star to the case of a higher central spin of size S N/2, where N is the number of sites in the XXX ring. Following [13], in which the coherence dynamics of a spin-1/2 Heisenberg star in the presence of an external magnetic was studied, we first describe how to block-diagonalize a spin-S Heisenberg star based on the Bethe ansatz solutions of the XXX ring. The dimensions of the resultant block Hamiltonians are at most 2S + 1.…”

Section: Introductionmentioning

confidence: 99%

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

Li¹,

Wu²

2022

Commun. Theor. Phys.

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We generalize the Heisenberg star consisting of a spin-1/2 central spin and a homogeneously coupled spin bath modeled by the XXX ring [Richter J and Voigt A 1994 \emph{J. Phys. A: Math. Gen.} \textbf{27} 1139-1149] to the case of arbitrary central-spin size $S<N/2$, where $N$ is the number of bath spins. We describe how to block-diagonalize the model based on the Bethe ansatz solution of the XXX ring, with the dimension of each block Hamiltonian $\leq 2S+1$. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each $l$-subspace with $l$ being the total angular momentum of the bath. Both the eigenenergies and the sub-ground states have distinct structures depending whether $S\leq l$ or $l<S$. The absolute ground-state energy and the corresponding $l$ as functions of the intrabath coupling are numerically calculated for $N=16$ and $S=1,2,\cdots,7$ and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. We then study the dynamics of the antiferromagnetic order within an XXX bath prepared in the N\'eel state. Effects of the initial state of the central spin, the value of $S$, and the system-bath coupling strength on the staggered magnetization dynamics are investigated. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, 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 anisotropy of the intrabath coupling.

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Section: Introductionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

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

Li¹,

Wu²

2022

Commun. Theor. Phys.

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“…[1] It is closely related to the central spin model [2,3] and BCS model, [4][5][6][7][8][9] which has been widely used in the study of metallic nanoparticles, [10] quantum dots, [11] noisy spins, [12] Rydberg atoms, [13] and so on. Based on the exact solutions of the Gaudin model, its correlation functions, [14] quantum dynamics [15][16][17][18] and coherence [19] have always been the focus of research.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions*

Wen¹,

Zhang²

2021

Chinese Phys. B

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We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore, it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.

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“…By passing we mention that the coherence dynamics from the thermal bath state of a spin-1/2 Heisenberg star in the presence of an external magnetic field was recently studied in Ref. [20].…”

mentioning

confidence: 99%

“…For J = J ′ and S = 1/2, H reduced to the model studied in Ref. [20], which conserves L 2 . If one further sets J = 0, then H is reduced to a qubit−big-spin model [14], whose dynamics can be analytically solved by using either a recurrence method [14] or an interaction-picture method [15].…”

mentioning

confidence: 99%

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

Li,

2022

Preprint

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is an interacting central spin model composed of a spin-1/2 central spin and a homogeneously coupled XXX ring. In this work, we generalize the spin-1/2 Heisenberg star to the case of arbitrary S < N/2, where S is the size of the central spin and N is the number of spins-1/2 in the XXX spin bath. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each l-subspace with l being the total angular momentum of the bath. The absolute ground-state energy and the corresponding bath angular momentum l as functions of the intrabath coupling are numerically calculated for N = 16 and S = 1, 2, • • • , 7 and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath initially prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, 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 anisotropy of the intrabath coupling.

show abstract

Coherence of an extended central spin model with a coupled spin bath

Cited by 7 publications

References 41 publications

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

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

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions*

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

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