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arXiv:1307.1325

Distribution of quantum discord in Heisenberg Antiferromagnets

Aritra Kundu, V. Subrahmanyam

Published Jul 4, 2013• 0 citations
arXivHTMLPDF

Abstract

The quantum discord, which quantifies the amount of quantum correlations present between parts of a system, is investigated for antiferromagnetic spin systems. The discord for a pair of spins in the many-spin ground state is related to the diagonal and off-diagonal spin-spin correlation functions and the local magnetization. For isotropic and translationally invariant states, the discord is shown to be a function of the diagonal correlation function only. Thus, near a thermal/quantum critical point, the discord for a pair of spins shows long-range behavior, analogously of the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the the ground state of the Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. The conditional entropy distribution over all possible the measurement basis is investigated. For the isotropic model, the distribution is just a delta-function, whereas it has a twin-peak structure for anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.

DOI
10.48550/arxiv.1307.1325

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The quantum discord, which quantifies the amount of quantum correlations present between parts of a system, is investigated for antiferromagnetic spin systems. The discord for a pair of spins in the many-spin ground state is related to the diagonal and off-diagonal spin-spin correlation functions and the local magnetization. For isotropic and translationally invariant states, the discord is shown to be a function of the diagonal correlation function only. Thus, near a thermal/quantum critical point, the discord for a pair of spins shows long-range behavior, analogously of the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the the ground state of the Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. The conditional entropy distribution over all possible the measurement basis is investigated. For the isotropic model, the distribution is just a delta-function, whereas it has a twin-peak structure for anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.
The quantum discord, which quantifies the amount of quantum correlation present between parts of a system, is investigated for spin systems. The discord for a pair of spins in the many-spin ground state, computed by minimizing the conditional entropy of the two spins, is related to the diagonal and off-diagonal spin–spin correlation functions and the local magnetization. We show that for isotropic and translationally invariant states, the discord depends only on the diagonal spin correlation function. Thus, near a thermal/quantum critical point, the pairwise discord exhibits long-range behavior, analogously to the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the ground state of the anisotropic Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. We also investigate, from exact numerical diagonalization, the distribution of conditional entropies as the measurement basis is varied. For the isotropic model, the conditional entropy distribution is a δ-function, whereas it has a twin-peak structure for the anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.
The correlations between a pair of spins in a many-spin state encoded in the diagonal and off-diagonal spin–spin correlation functions. These spin functions determine the quantum correlation measures, like pair-wise concurrence, quantum discord and other measures of quantum information. We show that for isotropic and translationally invariant states, the quantum correlations depend only on the diagonal spin correlation function. The pair concurrence shows a strict short-ranged behavior. The distribution of concurrence for a random W-like state exhibits a long tail for both time-reversal invariant states and for states that break the time reversal. The quantum discord can be related to the diagonal spin correlation function. As the spin function is long range close to a critical point, analogously the quantum discord exhibits a long range behavior. For the isotropic state, the conditional entropy distribution is a Dirac delta function, whereas it has a twin-peak structure for the anisotropic model.
Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important and active branch of research in the field of quantum information theory. Investigation of non-classical correlations in condensed matter systems gives important insights about the characteristics of these systems. In particular, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to the peculiar behavior of correlations near these points. In this thesis, we have investigated two distinct quantum spin models from the perspective of correlations and, we have discussed the correlation content of an important subclass of bipartite states. We start by an analytical calculation of the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in rotationally invariant states the amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have compared their quantum discord with entanglement and seen that quantum discord is higher than the entanglement. Next, we have investigated the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We have demonstrated that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement. Finally, we have investigated various thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We have shown that the ability of the considered measures to estimate the critical points of this system at finite temperature strongly depends on the anisotropy parameter of the Hamiltonian. Furthermore, we have studied the effect of temperature on long-range correlations of the XY chain.
Abstract We investigate the ground-state quantum correlations in the spin-1/2 XX chain with anisotropic four-spin interaction (AFSI), employing an exact analytical approach via fermionization. The phase diagram of the system hosts three distinct quantum critical lines that separate non-trivial topological phases characterized by winding numbers ν = ±1 and ν = ±3. To probe the system’s critical behavior and topological nature, we analyze two key quantum correlation measures: concurrence and quantum discord between nearest-neighbor spin pairs. Our results reveal that while concurrence is limited in detecting all critical lines particularly in phases with higher winding numbers, quantum discord successfully identifies all quantum phase transitions, either through cusps or discontinuities in its first derivative. Furthermore, quantum discord assumes larger values in topological phases with lower winding numbers, suggesting that the structure and localization of quantum correlations are influenced by topological order. These findings underscore the effectiveness of quantum discord as a robust diagnostic tool for both criticality and topology in many-body quantum systems. Our results offer valuable insight for advancing correlation-based techniques in quantum information science and highlight the potential role of topological spin chains in future quantum technologies.
Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.
Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.