We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord , we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.
In this paper, we study global quantum discord (GQD) in infinite-size spin chains. For this purpose, in the framework of matrix product states (MPSs), we propose an effective procedure to calculate GQD (denoted as Gn) for consecutive n-site subchains in infinite chains. For a spin-1/2 three-body interaction model, whose ground state can be exactly expressed as MPSs, We use the procedure to study Gn with n up to
24. Then for a spin-1/2 XXZ chain, we firstly use infinite time-evolving block decimation (iTEBD) algorithm to obtain the approximate wavefunction in the from of MPSs, and then figure out Gn with n up to
18. In both models, Gn shows an interesting linear growth as the increase of n, that is, Gn = k*n+b. Moreover, in non-critical regions the slope
k of Gn converges very fast, while in critical regions it converges relatively slow, and the behaviors are explained in a clear physical picture with the short-range and long-range correlations. Based on these results, we propose to use Gn/n to describe the global correlations in infinite chains. Gn/n has twofold physical meanings. Firstly, it can be regarded as "global discord per site", very similar to "energy per site" or "magnetization per site" in quantum magnetic systems. Secondly, Gn/n (when n is large enough) describes the quantum correlation between a single site and an (n-1)-site block. Then we successfully apply our theory to an exactly soluble infinite-size spin XY chain which is beyond the matrix product formula, and the Hamiltonian can reduce to the transverse-field Ising model and the XX model. The relation between GQD and quantum phase transitions in these models is discussed.
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 model, the
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
T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
One-dimensional spin-
21 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.
We study the scaling of quantum discord (a measure of quantum correlation beyond entanglement) in spin models analytically and systematically. We find that at finite temperature the block scaling of quantum discord satisfies an area law for any two-local Hamiltonian. We show that generically and heuristically the two-site scaling of quantum discord is similar to that of correlation functions. In particular, at zero temperature it decays exponentially and polynomially in gapped and gapless (critical) systems, respectively; at finite temperature it decays exponentially in both gapped and gapless systems. We compute the two-site scaling of quantum discord in the
XXZ chain, the
XY chain (in a magnetic field), and the transverse field Ising chain at zero temperature.
Pairwise quantum discord (QD) and classical correlation (CC) are studied in the
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.
The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. In this model, many entanglement and correlation measures, except the macroscopic multispecies entanglement measure, do not show true singular behavior in the vicinity of the critical point, as seen in the transverse-Ising model ground state and related models. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multispecies entanglement measure to investigate multiparty entanglement, both analytically and numerically. The nearest-neighbor concurrence shows a peak structure as a function of magnetic field, near the critical point, for various values of the ratio of interaction strengths, but its derivative does not show a singular behavior close to the critical point. A similar behavior is shown by the quantum discord and the global entanglement. The multispecies entanglement shows a clear signature of the critical point behavior, and the first-order derivative shows a divergence near zero magnetic field, for equal interaction strengths.