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arXiv:cond-mat/0701490 · Physical Review A

Evolution of a quantum spin system to its ground state: Role of entanglement and interaction symmetry

Shengjun Yuan, Mikhail I. Katsnelson, Hans A. De Raedt

Published May 18, 2007• 20 citations
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Abstract

We study the decoherence of two ferro- and antiferromagnetically coupled spins that interact with a frustrated spin-bath environment in its ground state. The conditions under which the two-spin system relaxes from the initial spin-up--spin-down state toward its ground state are determined. It is shown that the two-spin system relaxes to its ground state for narrow ranges of the model parameters only. It is demonstrated that the symmetry of the coupling between the two-spin system and the environment has an important effect on the relaxation process. In particular, we show that, if this coupling conserves the magnetization, the two-spin system readily relaxes to its ground state, whereas a nonconserving coupling prevents the two-spin system from coming close to its ground state.

DOI
10.1103/physreva.75.052109

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We study the decoherence of two ferro- and antiferromagnetically coupled spins that interact with a frustrated spin-bath environment in its ground state. The conditions under which the two-spin system relaxes from the initial spin-up--spin-down state toward its ground state are determined. It is shown that the two-spin system relaxes to its ground state for narrow ranges of the model parameters only. It is demonstrated that the symmetry of the coupling between the two-spin system and the environment has an important effect on the relaxation process. In particular, we show that, if this coupling conserves the magnetization, the two-spin system readily relaxes to its ground state, whereas a nonconserving coupling prevents the two-spin system from coming close to its ground state.
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This Letter studies the decoherence in a system of two antiferromagnetically coupled spins that interact with a spin bath environment. Systems are considered that range from the rotationally invariant to highly anisotropic spin models, have different topologies and values of parameters that are fixed or are allowed to fluctuate randomly. We explore the conditions under which the two-spin system clearly shows an evolution from the initial spin-up - spin-down state towards the maximally entangled singlet state. We demonstrate that frustration and, especially, glassiness of the spin environment strongly enhances the decoherence of the two-spin system.
We study the decoherence of two coupled spins that interact with a spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. For the anisotropic spin bath, changing the connectivity or coupling strength changes the decoherence of the central system from Gaussian to exponential decay law. The initial state of the environment is shown to affect the decoherence process in a qualitatively significant manner.
We study the decoherence process induced by a spin chain environment on a central spin consisting of R spins and we apply it on the dynamics of quantum correlations (QCs) of three interacting qubits. In order to see the impact of the initial prepared state of the spin chain environment on the decoherence process, we assume the spin chain environment prepared in two main ways, namely, either the ground state or the vacuum state in the momentum space. We develop a general heuristic analysis when the spin chain environment in prepared in these states, in order to understand the decoherence process against the physical parameters. We show that the decoherence process is mainly determined by the choice of the initial prepared state, the number of spin of the chain, the coupling strength, the anisotropy parameter and the position from the quantum critical point. In fact, in the strong coupling regime, the decoherence process does not appear for the environment prepared in the vacuum state and it behaves oscillatory in the case of evolution from ground state. On the other hand, in the weak coupling regime and far from the quantum critical point, decoherence induced by the ground state is weaker than that of the vacuum state. Finally, we show that, QCs are completely shielded from decoherence in the case of evolution from the W state and obey the same dynamics as the decoherence factors for the GHZ state.
The quantum entanglement, discord, and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied. The effects of the important physical parameters including the coupling strength of two spins, the interaction strength between the intermediate spin and the spin bath, the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases. The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state. At finite temperature, we find that coherence is more robust than quantum discord, which is better than entanglement, in terms of resisting the influence of environment. Therefore, quantum coherence is more tenacious than quantum correlation as an important resource.
We investigate the reduced dynamics of two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain. By using the method of time-dependent density matrix renormalization group (t-DMRG), it is shown that when the spin bath is in an ordering state, the reduced dynamics of qubits strongly depends on the range of the spin chain that qubits coupled to. Only for ordering spin baths, both decoherence and entanglement show qualitatively different behaviors when the coupling range changes. In particular, In particular, we find that in the parametic regime where there is no ordering in the bath, the coupling range is irrelevant. On the other hand, for ordering spin baths, when the coupling range increases from local coupling to infinite range coupling, the reduced dynamics of qubits exhibits a transition in which initially entangled states no longer suffers from the entanglement sudden death when the coupling range is large.