We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density matrices displaying Z2 symmetry. As an illustration, we analyze both the XXZ and the transverse field Ising models. Finite-size as well as infinite chains are investigated and the quantum criticality is discussed. Moreover, we identify the spin functions that govern the correlations. As a further example, we also consider correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick model. It is then shown that both classical correlation and quantum discord exhibit signatures of the quantum phase transitions.

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose non-analyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signalled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.PACS numbers: 03.65. Ud,75.10.Pq Recently, a great deal of effort has been devoted to the understanding of the connections between quantum information [1] and the theory of quantum critical phenomena [2]. A key novel observation is that quantum entanglement can play an important role in a quantum phase transition (QPT) [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In particular, for a number of spin systems, it has been shown that QPTs are signalled by a critical behavior of bipartite entanglement as measured, for instance, in terms of the concurrence [17]. For the case of second-order QPTs (2QPTs), the critical point was found to be associated to a singularity in the derivative of the ground state concurrence, as first illustrated, for the transverse field Ising chain, in Ref. [3], and generalized in Refs. [4,5,6] (see Refs. [7,8,9,10,11] for an analysis in terms of other entanglement measures). In the case of first-order QPTs (1QPTs), discontinuities in the ground state concurrence were shown to detect the QPT [12,13,14]. The studies conducted to date are based on the analysis of particular many-body models. Hence the general connection between bipartite entanglement and QPTs is not yet well understood. The aim of this work is to discuss, in a general framework, how bipartite entanglement can be related to a QPT characterized by nonanalyticities in the energy.Expectation values and the reduced density matrix.-The most general Hamiltonian of non-identical particles, up to two-body interactions, readswhere {|α i } is a basis for the Hilbert space, α, β, γ, δ ∈ {0, 1, ..., d − 1}, and i, j enumerate N "qudits" (dlevel systems).Let E = ψ|H|ψ be the energy in a non-degenerate eigenstate |ψ of the Hamiltonian. The two-spin reduced density operatorρ ij is given byρ ij = m m|ψ ψ|m , with m running over all the d N −2 orthonormal basis vectors, excluding qudits i and j.ρ ij has a d 2 × d 2 matrix representation ρ ij , with elements ρ with U(ij) denoting a d 2 × d 2 matrix whose elements are, where N i is the number of qudits that qudit i interacts with, and δ j βδ is the Kronecker symbol on qudit j. Clearly, Eq. (2) holds not only for the Hamiltonian operator but for any observable. Indeed, it turns out that the expectation value (or eigenvalue, for an eigenstate) of any two-qudit observable in an arbitrary state |ψ is a ...

We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.Comment: v4: 13 pages, 1 figure. Published version. v3: Time condition for adiabaticity improved and references update

We propose a global measure for quantum correlations in multipartite systems, which is obtained by suitably recasting the quantum discord in terms of relative entropy and local von Neumann measurements. The measure is symmetric with respect to subsystem exchange and is shown to be non-negative for an arbitrary state. As an illustration, we consider tripartite correlations in the Werner-GHZ state and multipartite correlations at quantum criticality. In particular, in contrast with the pairwise quantum discord, we show that the global quantum discord is able to characterize the infinite-order quantum phase transition in the Ashkin-Teller spin chain.

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SUN Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate hA 2 i, which has attracted much attention in the Landau gauge.