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arXiv:1206.4847 · Chinese Physics Letters

Quantum Discord and Entanglement in Heisenberg XXZ Spin Chain after Quenches

Jie Ren, Yin‐Zhong Wu, Shiqun Zhu

Published Jun 1, 2012• 11 citations
arXivHTMLPDF

Abstract

Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of an one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.

DOI
10.1088/0256-307x/29/6/060305

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Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of an one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.
The quantum entanglement dynamics of a one-dimensional spin-1/21/21/2 anisotropic XXZ\mathit{XXZ}XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.
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The long-range entanglement dynamics of an one-dimensional spin-1/2 anisotropic XXZ model are studied using the method of the adaptive time-dependent density-matrix renormalization-group. The long-range entanglement can be generated when a local quench on one of boundary bonds is performed in the system. The anisotropic interaction has a strong influence both on the maximal value of long-range entanglement and the time of reaching the maximum long-range entanglement. The local coupling has a notable impact on the long-range entanglement, but it can be neglected in the time of reaching the maximal long-range entanglement.
We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
We study the dynamics and the asymptotic behaviors of quantum discord in a one-dimensional XY model coupled through time-dependent nearest-neighbor interactions and in the presence of a time-dependent magnetic field. We find that the time evolution of the nearest-neighbor quantum discord in this system shows non-ergodic behaviors but is asymptotic to its steady value at the long-time limit. The zero-temperature asymptotic behaviors of quantum discord is only determined by the ratio between the coupling parameter and magnetic field, whereas the finite-temperature asymptotic behaviors determined by both of them. These asymptotic behaviors are sensitive not only to the initial values of the coupling parameter and magnetic field, but also to the final values. It is interesting to note that quantum discords are more robust than entanglement against the effect of temperature. We also find particular parameter regimes, where the nearest-neighbor quantum discord is enhanced significantly.
The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.