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arXiv:1710.05390 · Physical Review A

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Salimeh Mahdavifar, S. Mahdavifar, Rouhollah Jafari

Published Nov 2, 2017• 36 citations
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Abstract

One-dimensional spin-$\frac{1}{2}$ systems are well-known candidates to study the quantum correlations between particles. In condensed matter physics, studies often are restricted to first-neighbor particles. In this work, we consider the one-dimensional $XXZ$ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature by using the analytical approach proposed by Caux et al. [Phys. Rev. B 68, 134431 (2003)]. We compare the efficiency of the quantum discord (QD) with respect to the entanglement in the detection of critical points as the neighboring spin pairs go farther than the next-nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the second neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast with the pairwise entanglement, two-site QD is effectively long range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal QD between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.

DOI
10.1103/physreva.96.052303

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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.
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 extend the program initiated by T. Werlang et al. [Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ\mathit{XXZ}XXZ model, the XY\mathit{XY}XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest neighbors and also study the behavior of entanglement and quantum discord for second nearest neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite TTT, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a "magnetic-entanglement" behavior that starts from an entangled field around the saturation field.
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.
Pairwise quantum discord (QD) and classical correlation (CC) are studied in the XY\mathit{XY}XY spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.