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arXiv:1011.5309 · Europhysics Letters (EPL)

Quantum discord surge heralds entanglement revival in an infinite spin chain

Himadri Shekhar Dhar, Rupamanjari Ghosh, Aditi Sen(De), Ujjwal Sen

Published May 1, 2012• 20 citations
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Abstract

A measure of quantum correlation defined from an information-theoretic perspective, namely, quantum discord, is applied to study the time-evolved nonequilibrium state of the infinite anisotropic quantum XY spin chain in a transverse time-dependent field. In particular, we probe whether the collapse and revival of nearest-neighbor entanglement of the state seen with a varying initial applied field strength, at a fixed evolution time, may be predicted from the behavior of the quantum correlation measure. For this quantum many-body system, realizable with currently available technology, we find that the revival of entanglement of the evolved state occurs if there is an increase in quantum discord in the vicinity of entanglement collapse.

DOI
10.1209/0295-5075/98/30013

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A measure of quantum correlation defined from an information-theoretic perspective, namely, quantum discord, is applied to study the time-evolved nonequilibrium state of the infinite anisotropic quantum XY spin chain in a transverse time-dependent field. In particular, we probe whether the collapse and revival of nearest-neighbor entanglement of the state seen with a varying initial applied field strength, at a fixed evolution time, may be predicted from the behavior of the quantum correlation measure. For this quantum many-body system, realizable with currently available technology, we find that the revival of entanglement of the evolved state occurs if there is an increase in quantum discord in the vicinity of entanglement collapse.
The nearest-neighbor entanglement of the evolved state of an asymmetric quantum XY spin chain, in a transverse time-dependent field, exhibits criticalities (dynamical phase transitions) as the initial field parameter is varied at a given fixed time. After a discussion of the dynamical phase transition, we investigate the extent to which the role of an information-theoretic quantum correlation measure, called quantum discord, can be used to understand the entanglement dynamics in this spin model. We show that quantum discord can be associated with the collapse and revival of nearest-neighbor entanglement exhibited in the critical behavior. This behavior of quantum discord leads to the broader question of whether certain classes of measures of nonclassical correlation can help to understand the non-generic features of entanglement in a given system.
The time dynamics of quantum correlations in the quantum transverse anisotropic XYXYXY spin chain of infinite length is studied at zero and finite temperatures. The evolution occurs due to the instantaneous quenching of the coupling constant between the nearest-neighbor spins of the model, which is performed either within the same phase or across the quantum phase-transition point connecting the order-disorder phases of the model. We characterize the time-evolved quantum correlations, viz., entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the quenching scheme. We show that the system is endowed with enhanced nearest-neighbor bipartite quantum correlations compared to that of the initial state, when quenched from the ordered to the deep disordered phase. However, nearest-neighbor quantum correlations are almost washed out when the system is quenched from the disordered to the ordered phase with the initial state being at the zero temperature. We also identify the condition for the occurrence of enhanced bipartite correlations when the system is quenched within the same phase. Moreover, we investigate the bipartite quantum correlations when the initial state is a thermal equilibrium state with finite temperature, which reveals the effects of thermal fluctuation on the phenomena observed at zero temperature. Finally, an analogous analysis is carried out for zero-temperature next-nearest-neighbor quantum correlations.
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.
We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one-way information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All of these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.
We investigate the dynamics of a spin chain with Kitaev-type interaction in a transverse magnetic field, for both a constant field and a periodically kicked field. We investigate analytically the revivals in the dynamical behavior of the magnetization, and measures of local quantum correlations, the concurrence measure of the entanglement, and the quantum discord. The magnetization revivals are seen even for larger chain lengths, with reduced revival peaks, both near and away from the critical point at zero magnetic field. The quantum entanglement and correlation measures, contrary to the expected behavior, exhibit reduced quantum correlations in the critical region, compared to the region away from the critical point. The concurrence is larger than the quantum discord away from the critical region. The pair entanglement is near zero for all times in the critical region, though the quantum discord is nonzero, capturing the underlying diagonal correlations. The kicked magnetic field dynamics shows similar evolution for the magnetization and quantum correlations. For special values of the kicking period, the concurrence shows alternates between zero and nonzero values for successive kicks in the noncritical region.
We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one way-information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.