Exact diagonalization of the XY-Hamiltonian of open linear chains with periodic coupling constants and its application

Feldman, K. E.

doi:10.1088/0305-4470/39/5/003

Cited by 16 publications

(17 citation statements)

References 13 publications

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“…[34], the analytical expressions are complicated. For this reason, we will employ the numerical calculation to investigate whether the Lyapunov control is suited to the case for the period l > 3.…”

Section: Scalability and Discussionmentioning

confidence: 99%

“…Finally, we have shown that replacing the fast time-varying control fields with square wave pulses are possible, which simplifies the experimental realization. [34,36,37]. When l = 3 and d = 2, the matrix reads, …”

Section: Discussionmentioning

confidence: 99%

“…To be specific, we set the period l = 3. The solutions of eigenvalues and eigenstates of this general linear chain with open boundary have been given in appendix [34]. We select a specific eigenstate of the Hamiltonian H 0 so that the target state satisfies the condition | M|λ f | ∼ 1.…”

Section: Target Statementioning

confidence: 99%

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Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control

Shi¹,

Zhao²

2015

Phys. Rev. A

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Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at non-stationary state (or information) transfer from the first spin to the end spin at a fixed time. The present scheme possesses the following advantages. First, the scheme does not require precise manipulations of the control time. Second, it is robust against uncertainties in the initial states and fluctuations in the control fields. Third, the controls are exerted only on the boundary sites of the chain. It works for variable spin-1/2 chains with different periodic structures and has well scalability. The feasibility to replace the control fields by square pules is explored, which simplifies the realization in experiments.

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Section: Scalability and Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control

Shi¹,

Zhao²

2015

Phys. Rev. A

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“…The physics behind the above result, is that as the distance between the weakened bonds becomes larger, then lower values of J are required to produce the same effect and, in the limit of very large n then J c approaches 0 which indicates that it effectively requires cutting the chain in order to produce the same result. The analytical treatment and proof of this relation is beyond the scope of the present work and will be presented elsewhere as it involves the non-trivial diagonalisation of a chain of n spins with periodically modulated couplings and periodic boundary conditions 27 . The case of a single site with transverse field in an n-periodic chain has been investigated analytically, e.g., in Ref.…”

Section: E Generalization To N-site Periodmentioning

confidence: 99%

Entanglement scaling and spatial correlations of the transverse-field Ising model with perturbations

2017

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We study numerically the entanglement entropy and spatial correlations of the one-dimensional transverse-field Ising model with three different perturbations. First, we focus on the out-of-equilibrium steady state with an energy current passing through the system. By employing a variety of matrix-product state based methods, we confirm the phase diagram and compute the entanglement entropy. Second, we consider a small perturbation that takes the system away from integrability and calculate the correlations, the central charge, and the entanglement entropy. Third, we consider periodically weakened bonds, exploring the phase diagram and entanglement properties first in the situation when the weak and strong bonds alternate (period two bonds) and then the general situation of a period of n bonds. In the latter case we find a critical weak bond that scales with the transverse field as J'(c)/J = (h/J)(n), where J is the strength of the strong bond, J' is that of the weak bond, and h is the transverse field. We explicitly show that the energy current is not a conserved quantity in this case

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“…In this paper we will consider the anisotropic XY-model in a transverse field on the inhomogeneous periodic (closed) chain consisting of N cells composed of n sites, whose version on the open chain has been recently addressed by Feldman [9]. It has also been studied by Tong and Zhong [10] and Derzhko et al [11], who have restricted their analysis to the study of the thermodynamic properties.…”

Section: Introductionmentioning

confidence: 99%