We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z_{2} symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ>0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to sqrt[n] for sufficiently large values of n.
Abstract We study the post-quench unitary dynamics of a quantum sunburst spin model, composed of a transverse-field quantum Ising ring which is suddenly coupled to a set of independent external qubits along the longitudinal direction, in a way to respect a residual translation invariance and the Ising Z 2 symmetry. Starting from the different equilibrium quantum phases of the system, we characterize the decoherence and the energy storage in the external qubits, which may be interpreted as a probing apparatus for the inner Ising ring. Our results show that, in proximity of the quantum transitions of the Ising ring, either first-order or continuous, it is possible to put forward dynamic finite-size scaling frameworks which unveil peculiar scaling regimes, depending on the way in which the large-size limit is taken: either by fixing the number n of probing qubits, or their interspace distance b . In any case, the dependence of the various observables on n can be reabsorbed into a redefinition of the quench parameter by a n prefactor. We also address the role of a nearest-neighbor coupling between the external qubits.
We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered XXZ model with disorder strength putting it in the many-body localized phase.
We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity to a quantum first-order or continuous-phase transition. Although the approach is quite general, we consider
d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information-oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchange between the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing system size.
We study the energy-transfer process in the recently proposed sunburst quantum Ising model, which consists of two interacting integrable systems: a transverse Ising chain with a very small transverse field and a finite number of external isolated qubits. We show that in this model of the quantum battery, coupling between the battery and charger can be used to optimize the ergotropy, which is the maximum amount of energy that can be extracted from the battery. At the same time, maximum charging power increases with the coupling strength, allowing for the simultaneous optimization of both ergotropy and charging power in the strong-coupling limit. Furthermore, we show that both ergotropy and charging power are independent of the initial state of the charger.
We study the nonequilibrium dynamics of a homogeneous quantum Ising ring after a quench, in which the transverse field
g suddenly changes from zero to a nonzero value. The long-timescale reduced dynamics of a single spin and of two nearest-neighbor spins, which involves the evaluation of expectation values of odd operators that break the fermion parity, is exactly obtained for finite-size but large rings through the use of a recently developed Pfaffian method [N. Wu, Phys. Rev. E 101, 042108 (2020)]. Time dependence of the transverse and longitudinal magnetizations (${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{z}\ensuremath{\rangle}}_{t}$ and ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x,y}\ensuremath{\rangle}}_{t}$), single-spin purity, expectation value of the string operator ${X}_{j}={\ensuremath{\prod}}_{l=1}^{j\ensuremath{-}1}{\ensuremath{\sigma}}_{l}^{z}{\ensuremath{\sigma}}_{j}^{x}$ (${\ensuremath{\langle}{X}_{j}\ensuremath{\rangle}}_{t}$), several equal-time two-site correlators (${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x,z}{\ensuremath{\sigma}}_{j+1}^{x,z}\ensuremath{\rangle}}_{t}$, ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x}{\ensuremath{\sigma}}_{j+1}^{y}\ensuremath{\rangle}}_{t}$, and ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x}{\ensuremath{\sigma}}_{j+1}^{z}\ensuremath{\rangle}}_{t}$), and pairwise concurrence after quenches to different phases are numerically studied. Our main findings are that (i) The expectation value of a generic odd operator approaches zero in the long-time limit; (ii) ${\ensuremath{\langle}{X}_{j}\ensuremath{\rangle}}_{t}$ exhibits
j-independent exponential decay for a quench to
g=1 and the time at which ${\ensuremath{\langle}{X}_{j}\ensuremath{\rangle}}_{t}$ reaches its first maximum scales linearly with
j; (iii) The single-spin purity dynamics is mainly controlled by ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x}\ensuremath{\rangle}}_{t}$ (${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{z}\ensuremath{\rangle}}_{t}$) for a quench to
g<1 ($g\ensuremath{\ge}1$). For quenches to the disordered phase with $g\ensuremath{\gg}1$, the single-spin tends to be in the maximally mixed state and the transverse and longitudinal correlators ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{z}{\ensuremath{\sigma}}_{j+1}^{z}\ensuremath{\rangle}}_{t}$ and ${\ensuremath{\langle}{\ensuremath{\sigma}}_{j}^{x}{\ensuremath{\sigma}}_{j+1}^{x}\ensuremath{\rangle}}_{t}$, respectively, approaches $\ensuremath{-}0.25$ and
0.5 in the thermodynamic limit; (iv) The nearest-neighbor entanglement acquires a finite plateau value that increases with increasing
g, and approaches a saturated value $\ensuremath{\sim}0.125$ for $g\ensuremath{\gg}1$.
We investigate the entanglement properties of finite spin rings, with noncollinear Ising interaction between nearest neighbors. The orientations of the Ising axes are determined either by the spin position within the ring (model
A) or by the direction of the bond (model
B). In both cases, the considered spin Hamiltonians have a point-group symmetry instead of the translation invariance that characterizes spin rings with collinear Ising interaction. The ground state of these models exhibit remarkable entanglement properties, resembling Greenberger-Horne-Zeilinger (GHZ)-like states in the absence of an applied magnetic field (model
B). Besides, the application of a homogeneous magnetic field allows to modify qualitatively the character of the ground-state entanglement, switching from multipartite to pairwise quantum correlations (both models
A and
B).