Global quantum correlations in finite-size spin chains

Abstract

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.Entanglement and criticality in quantum many-body systems have been shown to be strongly and intimately connected concepts [1,2]. The body of work performed with the aim of grasping the implications that critical changes in the ground state of a given Hamiltonian model have for the sharing of entanglement by the parties of a quantum many-body systems is now quite substantial [3]. This has resulted in important progress in our understanding of the interplay between critical phenomena of interacting many-body systems and the setting up of genuinely quantum features. In turn, such success has proven the effectiveness of the cross-fertilization of quantum statistical mechanics by techniques and interpretations that are typical of quantum information theory.Yet, it has recently emerged that the way correlations of non-classical nature manifest themselves is not necessarily coincident with entanglement, and a much broader definition of quantum correlations should be given [4,5]. This is encompassed very effectively in the formulation of so-called quantum discord as a measure striving to capture the above-mentioned broadness of quantum correlations [6]. In analogy with the case of entanglement, the relation between quantum discord and the features of quantum many-body models is fundamentally interesting for the understanding of the role that the settlement of quantumness of correlations play in determining the critical properties of such models. A systematic analysis in this sense, which has only recently been considered [7][8][9][10][11][12][13], is thus highly desirable. This is even more important given that some of the investigations performed so far have indicated that quantum discord is more sensible than entanglement in revealing quantum critical points [9], even for systems that are not at zero temperature [14]. This is a particularly relevant result, whose validity should also be checked for models that are both finite sized and at finite temperature. The motivations for such an endeavor stem from the fact that, likely, the properties of quantum many-body systems will be addressed experimentally in systems consisting of, for instance, cold atoms loaded in optica...

General monogamy property of global quantum discord and the application

“…The behavior of bipartite and global correlations in the quantum spin chains, especially for Ising model, has attracted considerable interest. Recently, it is worth noting that the behavior of global quantum discord of a finite-size transverse field Ising model near its critical point has been studied [45]. Next, we also use Ising model with transverse filed as an example to show the application of the GQD.…”

Multipartite quantum and classical correlations in symmetric n-qubit mixed states

“…An alternative formulation that reduces the computational effort was given in Ref. [29], where the multiqubit projections were expressed in terms of local multiqubit rotations, R i (θ i , φ i ) = cos θ i1 1 + i sin θ i cos ϕ iσy + i sin θ i sin ϕ iσx applied to the separable eigenstates of ⊗ n i=1σ z . The minimization of Eq.…”

“…Considering the same physical process, in Ref. [28], we analyzed the behavior of multipartite quantum discord, using both the definition of global discord [12,29] and the measure of genuinely multipartite correlations [14]. The protocol consists of a series of swap operations between different eigenstates of a density matrix that is diagonal with respect to the Hamiltonian basis both at the beginning and at the end of the cycle.…”

Majorization Relation in Quantum Critical Systems

“…Our results are compared with the corresponding results using the Rényi entropy and the LOCC convertibility with assisted entanglement. [10], have also been used for detecting quantum phase transitions. Other investigations in entanglement spectra [11][12][13] and fidelity [14] as well as the fidelity susceptibility of the ground state show their abilities in exploring numerous phase transition points in various critical systems, as well.…”

“…For example, entanglements measured by concurrence [3], negativity [4], geometric entanglement [5], and von Neumann entropy [6,7] have been investigated in several critical systems. From another viewpoint of quantum correlations, other concepts in quantum information including mutual information [8], quantum discord [9] and global quantum discord [10], have also been used for detecting quantum phase transitions. Other investigations in entanglement spectra [11][12][13] and fidelity [14] as well as the fidelity susceptibility of the ground state show their abilities in exploring numerous phase transition points in various critical systems, as well.…”