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arXiv:1510.00685 · Physical Review A

Survival of time-evolved quantum correlations depending on whether quenching is across a critical point in an XY spin chain

Utkarsh Mishra, Debraj Rakshit, R. Prabhu

Published Apr 15, 2016• 10 citations
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Abstract

The time dynamics of quantum correlations in the quantum transverse anisotropic $XY$ 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.

DOI
10.1103/physreva.93.042322

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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 employ the mean-field approach in the fermionic picture of the spin-12\frac{1}{2}21​ XXZXXZXXZ chain to investigate the dynamics of bipartite quantum discord and concurrence under sudden quenching. In this case, when quenching is performed in the anisotropy from an initial value to the critical point, the quantum correlations show periodic cusps in time. Moreover, the first suppression (cusp) in quantum correlations can be explained in terms of the semiclassical picture of quasiparticle propagation. On the other hand, quenching to, as well as away from, the criticality point shows that the long time pairwise quantum discord gets enhanced from its initial state. Finally, we show that, in the gapped region, a quench in the transverse field displays survival of the next-nearest-neighbor quantum discord. Our results provide a further insight into the dynamical behavior of quantum correlations and their connections to quantum criticality.
We investigate the behaviour of quantum correlations (entanglement and quantum discord) for homogeneous XY model at absolute zero and at finite temperature. Study of this correlation measures of quenched disordered quantum spin models like the XY spin glass and random-field XY models is also reviewed. We show that quenched averaged quantum correlations can showcase the order-from-disorder phenomenon for finite-size systems and also when the system is in the thermodynamic limit. Though we find some regions with positive enhancement score. This order from disorder phenomena is more prominent when the system is in the finite temparature with some definite values of external parameter. We also look into correlation length. Correlation functions of ground states typically decay exponentially with the distance for quantum spin systems. In such systems, entanglement does not survive when |i-j| ≳ 3. However, quantum discord survives long lattice distances as it is not monogamous for this system. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY spin glass chains. We realize that there is practically neither diminution nor growth in entanglement length while quantum discord length increases significantly with the introduction of quenched disorder except near factorization point. Apart from that, we also investigate the scaling behaviour of quantum entanglement and quantum discord. We find that though entanglement follows finite size scaling close to quantum phase transition, scaling can't be done for quantum discord.
We study the dynamics of entanglement in the infinite asymmetric XYXYXY spin chain, in an applied transverse field. The system is prepared in a thermal equilibrium state (ground state at zero temperature) at the initial instant, and it starts evolving after the transverse field is completely turned off. We investigate the evolved state of the chain at a given fixed time, and show that the nearest-neighbor entanglement in the chain exhibits a critical behavior (which we call a dynamical phase transition), controlled by the initial value of the transverse field. The character of the dynamical phase transition is qualitatively different for short and long evolution times. We also find a nonmonotonic behavior of entanglement with respect to the temperature of the initial equilibrium state. Interestingly, the region of the initial field for which we obtain a nonmonotonicity of entanglement (with respect to temperature) is directly related to the position and character of the dynamical phase transition in the model.
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.
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 review recent studies on the measures of zero temperature quantum correlations namely, the quantum entanglement (concurrence) and discord present in the final state of a transverse XY spin chain following a quench through quantum critical points; the aim of these studies is to explore the scaling of the above quantities as a function of the quench rate. A comparative study between the concurrence and the quantum discord shows that their behavior is qualitatively the same though there are quantitative differences. For the present model, the scaling of both the quantities are given by the scaling of the density of the defect present in the final state though one cannot find a closed form expression for the discord. We also extend our study of quantum discord to a transverse Ising chain in the presence of a three spin interaction. Finally, we present a study of the dynamical evolution of quantum discord and concurrence when two central qubits, initially prepared in a Werner state, are coupled to the environmental XY spin chain which is driven through quantum critical points. The qualitative behavior of quantum discord and concurrence are found to be similar as that of the decoherence factor.