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arXiv:1607.02837 · Physical Review A

Non-Markovian dynamics in the extended cluster spin-1/2 XX chain

Maryam Mahmoudi, S. Mahdavifar, T. Mohammad Ali Zadeh, Mohammad Reza Soltani

Published Jan 30, 2017• 16 citations
arXivHTMLPDF

Abstract

We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2 $\mathit{XX}$ chain, equivalent to a one-dimensional spin-1/2 $\mathit{XX}$ model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.

DOI
10.1103/physreva.95.012336

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We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2 XX\mathit{XX}XX chain, equivalent to a one-dimensional spin-1/2 XX\mathit{XX}XX model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.
A thermodynamic limit chain of spin-1/2 particles with XX and three-spin interactions (TSI) is considered. Using the fermionization technique, the Hamiltonian of the chain with periodic boundary conditions is exactly diagonalized. In the ground-state phase diagram of the chain system, a quantum critical point separates the Luttinger liquid and chiral phases. Selecting one-spin as an open quantum system, the rest of the spins play the role of its environment. By choosing different initial states, we studied the dynamics of the entanglement between the open quantum system and its environment. In the initial state, the state of the open quantum system is a superposition of up and down states and the environment is polarized. The revival of the entanglement is observed in the whole range of interactions as an indicator of non-Markovian dynamics. Our exact results revealed that non-Markovian behavior is independent of the initial state. By tuning the initial state, the open quantum system will be completely entangled with the environment at a special time called entanglement-time, tE. The value of the mentioned entanglement-time decreased by increasing TSI. The signature of a quantum critical point is confirmed by investigating the long-time average of the entanglement and using the trace-distance as a witness of non-Markovianity.
One-spin and two-spin in a thermodynamic limit spin-1/2 chain as open quantum systems are considered. The dynamics of system is generated by XX Heisenberg interaction and three-spin interaction (TSI) among all the nearest three spins in the chain. Two variety Hamiltonians of the three-spin interaction are considered. Using the fermionization technique and calculating the trace distance, non-Markovianity as a function of the TSI is evaluated, and the results for the two different open quantum systems are compared. In addition, the time behavior of the probability amplitudes are studied. The results show that if all probability amplitudes except one of them will almost vanish after some time, the dynamics of the open quantum system will be Markovian. In the non-Markovian dynamics, more than one of the probability amplitudes fluctuate in time and will never reach zero value.
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We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled spin qubits with Dzyaloshinsky-Moriya interaction influenced by a locally external magnetic field along zzz-direction and coupled to bath spin-1/2 particles as independent non-Markovian environment. We find that with increasing DzD_{z}Dz​ and decreasing JzJ_{z}Jz​, the value of entanglement and quantum discord increase for both antiferromagnetic and ferromagnetic materials. Not that, this growth is more for the ferromagnetic materials. In addition, we perceive that entanglement and quantum discord decrease with increased temperature and increased coupling constants between reduced system and bath. But, strong quantum correlations within the spins of bath reduce decoherence effects. We discuss about type of the constituent material of the central spins that it can speedup the quantum information processing and as a result, we perceive that one can improve and control the quantum information processing with correct selection of the properties of the reduced system (JJJ, JzJ_{z}Jz​, DzD_{z}Dz​).
We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.
We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain’s dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.