Global entanglement and quantum criticality in spin chains

Abstract

Entanglement in quantum XY spin chains of arbitrary length is investigated via a recentlydeveloped global measure suitable for generic quantum many-body systems. The entanglement surface is determined over the phase diagram, and found to exhibit structure richer than expected. Near the critical line, the entanglement is peaked (albeit analytically), consistent with the notion that entanglement-the non-factorization of wave functions-reflects quantum correlations. Singularity does, however, accompany the critical line, as revealed by the divergence of the field-derivative of the entanglement along the line. The form of this singularity is dictated by the universality class controlling the quantum phase transition. [5,6,7,8], where it can play the role of a diagnostic of quantum correlations. Quantum phase transitions [9] are transitions between qualitatively distinct phases of quantum many-body systems, driven by quantum fluctuations. In view of the connection between entanglement and quantum correlations, one anticipates that entanglement will furnish a dramatic signature of the quantum critical point. From the viewpoint of quantum information, the more entangled a state, the more resources it is likely to possess. It is thus desirable to study and quantify the degree of entanglement near quantum phase transitions. By employing entanglement to diagnose many-body quantum states one may obtain fresh insight into the quantum many-body problem.To date, progress in quantifying entanglement has taken place primarily in the domain of bipartite systems [10]. Much of the previous work on entanglement in quantum phase transitions has been based on bipartite measures, i.e., focus has been on entanglement either between pairs of parties [5,6] or between a part and the remainder of a system [7]. For multipartite systems, however, the complete characterization of entanglement requires the consideration of multipartite entanglement, for which a consensus measure has not yet emerged.Singular and scaling behavior of entanglement near quantum critical points was discovered in important work by Osterloh and co-workers [6], who invoked Wootters' bipartite concurrence [11] as a measure of entanglement. In the present letter, we apply a recently-developed global measure that provides a holistic, rather than bipartite, characterization of the entanglement of quantum manybody systems. Our focus is on one-dimensional spin systems, specifically ones that are exactly solvable and

Criticality in correlated quantum matter

“…which has been recently studied in the context of entanglement [28]. The point (λ 1 = 0, λ 2 = 1) is the unstable isotropic XY fixed point; note that (λ 1 = 0, λ 2 = −1) has the same excitation spectrum.…”

Multipartite entanglement measures and quantum criticality from matrix and tensor product states

“…The first is GE which is geometrically defined as the distance between |ψ and the nearest separable state |φ [5,6], i.e., E(ψ) = − log Λ 2 max , Λ max = max | ψ|φ |…”

“…On the other hand, there are very few multipartite entanglement measures which can be used to characterize the QPTs, among which the global entanglement (GE) was proposed to probe the quantum criticality and has been tested for 1D quantum spin systems [5,6,7,8].…”

Reexamination of entanglement and the quantum phase transition

“…We further point out that QPTs can not always be diagnosed even by using the von Neumann entropy. As far as we know, there are some other measures of entanglement, say localizable entanglement [10] and global measure of entanglement [11]. Therefore, while the analyticity properties of concurrence and von Neumann entropy are not necessarily related to the existence of critical points, other measures of entanglement may work.…”

“…Quantum entanglement, as one of the most fascinating feature of quantum theory, has attracted much attention over the past decade, mostly because its nonlocal connotation [1] is regarded as a valuable resource in quantum communication and information processing [2]. Recently a great deal of effort has been devoted to the understanding of the connection between quantum entanglement and quantum phase transitions (QPTs) [3,4,5,6,7,8,9,10,11,12,13,14,15]. Quantum phase transitions [16] are transitions between qualitatively distinct phases of quantum many-body systems, driven by quantum fluctuations.…”