Separable and entangled states in the high-spin 
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 central spin model

Wu, Ning; Guan, Xi‐Wen; Links, Jon

doi:10.1103/physrevb.101.155145

Cited by 13 publications

(8 citation statements)

References 45 publications

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“…It is usually the case that g ′ j /g j = Λ, ∀j, where Λ measures the anisotropy of the system-bath coupling. In the case of J = J ′ = 0, the bath becomes noninteracting and we recover the usual Gaudin model that admits Bethe ansatz solutions under certain conditions [2,16,18,19].…”

Section: A Hamiltonianmentioning

confidence: 88%

“…The study of real-time dynamics of a composite system made up of a central spin and a coupled quantum spin bath is important for understanding many physical phenomena in condensed matter and statistical physics [1]. In particular, the Gaudin model [2] and its variants, which describe a central spin coupled to spin baths without intrabath coupling, play an important role in quantum decoherence [3][4][5][6][7][8][9][10], quantum information [11,12], quantum metrology [13], and even mathematical physics [14][15][16][17][18][19]. The dynamics of these noninteracting central spin models has been widely studied by many theoretical methods, including techniques based on the Bethe ansatz solutions [4,9,10,17,20], quantum master equations [5][6][7], density matrix renormalization group method [8], and so on.…”

Section: Introductionmentioning

confidence: 99%

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

Li,

Cao,

2021

Preprint

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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.

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Section: A Hamiltonianmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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

Li,

Cao,

2021

Preprint

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“…Recent work described in detail the collapse and revival dynamics of the homogeneous central spin model [30], and the partition of eigenstates between entangled and separable states [31,32].…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of Gaudin magnets

Chesi

Lin

et al. 2022

Commun. Theor. Phys.

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Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin-spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of Gaudin type.

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“…The central spin model, as an exactly solvable model, has played a vital role in quantitatively understanding decoherence problem and entanglement dynamics [33][34][35][36][37][38][39][40][41][42]. This model can be experimentally realized by superconductors [43], quantum dots [44][45][46], and nitrogenvacancy centers in diamond [47].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and work extraction in the central-spin quantum battery

Liu,

Shi,

Shi

et al. 2022

Preprint

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We consider a central-spin battery where N b central spins serve as battery cells and Nc bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the batterycharger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time ∝ 1/Nc, large extractable work, and √ Nc-improvement of charging power compared with the battery in the Tavis-Cummings limit. The above-mentioned results have also been numerically verified in multi-cell batteries. Our results pave the way to improve extractable work storage in the central-spin battery and highlight a competitive relation between the extractable work and the battery-charger entanglement.

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Separable and entangled states in the high-spin XX central spin model

Cited by 13 publications

References 45 publications

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

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

Quantum dynamics of Gaudin magnets

Entanglement and work extraction in the central-spin quantum battery

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