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Quantum Correlation in One Dimensional Spin Model

Sarnava Datta

Published Apr 1, 2017• 0 citations
OpenAlex

Abstract

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.

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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.
Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.
We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins--for classical and quantum correlations--is related to the quantum critical point in the corresponding ordered 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 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.
We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.
We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY\mathit{XY}XY spin-1/21/21/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX\mathit{XX}XX limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.