We compute the quantum correlation (quantum discord (QD)) and the entanglement (EoF) between nearest neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EoF and other thermodynamic quantities, spotlight the critical points associated to quantum phase transitions (QPT) for this model even at finite T . This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen. Quantum phase transition (QPT) is a purely quantum process [1] occurring at absolute zero temperature (T = 0), where no thermal fluctuations exist and hence no classical phase transition is allowed to occur. QPT is caused by changing the system's Hamiltonian, such as an external magnetic field or the coupling constant. These quantities are generally known as the tuning parameter. As one changes the Hamiltonian one may reach a special point (critical point) where the ground state of the system suffers an abrupt change mapped to a macroscopic change in the system's properties. This change of phase is solely due to quantum fluctuations, which exist at T = 0 due to the Heisenberg uncertainty principle. This whole process is called QPT. The paramagnetic-ferromagnetic transition in some metals [2], the superconductor-insulator transition [3], and superfluid-Mott insulator transition [4] are remarkable examples of this sort of phase transition.In principle QPTs occur at T = 0, which is unattainable experimentally due to the third law of thermodynamics. Hence, one must work at very small T , as close as possible to the absolute zero, in order to detect a QPT. More precisely, one needs to work at regimes in which thermal fluctuations are insufficient to drive the system from its ground to excited states. In this scenario quantum fluctuations dominate and one is able to measure a QPT.So far the theoretical tools available to determine the critical points (CP) for a given Hamiltonian assume T = 0. For spin chains, for instance, the CPs are determined studying, as one varies the tuning parameter, the behavior of either its magnetization, or bipartite [5] and multipartite [6] entanglement, or its quantum correlation (QC) [7]. By investigating the extremal values of these quantities as well as the behavior of their first and second order derivatives one is able to spotlight the CP. However, the T = 0 assumption limits a direct connection between these theoretical "CP detectors" and experiment. Indeed, if thermal fluctuations are not small enough excited states become relevant and the tools developed so far cannot be employed to clearly indicate the CP.In this Letter we remove this limitation and present a theoretical tool that is able to clearly detect CPs for QPTs at finite T . We show that the behavior of strictly QCs [8] at finite T , as gi...

We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime ∆ > 1, extending our previous results to the full parameter plane of the antiferromagnetic chain (∆ > −1 and arbitrary field h). The factorized formulae are numerically efficient and allow for taking the isotropic limit (∆ = 1) and the Ising limit (∆ = ∞). At the critical field separating the fully polarized phase from the Néel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite ∆ inducing unexpected crossover phenomena in the correlations. *

We communicate results on correlation functions for the spin-1/2 Heisenberg chain in two particularly important cases: (a) for the infinite chain at arbitrary finite temperature T, and (b) for finite chains of arbitrary length L in the ground state. In both cases we present explicit formulas expressing the short-range correlators in a range of up to seven lattice sites in terms of a single function ω encoding the dependence of the correlators on T (L). These formulas allow us to obtain accurate numerical values for the correlators and derived quantities like the entanglement entropy. By calculating the low T (large L) asymptotics of ω we show that the asymptotics of the static correlation functions at any finite distance are T(2) (1/L(2)) terms. We obtain exact and explicit formulas for the coefficients for up to eight sites.

We calculate the entropy and cooling rate of the antiferromagnetic spin-1/2 XXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and non-linear integral equations. The limiting case of the Ising chain (corresponding to infinitely large anisotropy) is presented for comparison. Our exact results for the Heisenberg chain are used as a crosscheck for the numerical exact diagonalization as well as Quantum Monte Carlo simulations and allow us to benchmark the numerical methods. Close to field-induced quantum phase transitions we observe a large magnetocaloric effect. Furthermore, we verify universal low-temperature power laws in the cooling rate and entropy, in particular linear scaling of entropy with temperature T in the gapless Luttinger-liquid state and scaling as √ T at field-induced transitions to gapped phases.

We study the isotropic Heisenberg chain with nearest and next-nearest neighbour interactions. The ground state phase diagram is constructed in dependence on the additonal interactions and an external magnetic field. The thermodynamics is studied by use of finite sets of non-linear integral equations resulting from integrabiliy. The equations are solved numerically and analytically in suitable limiting cases. We find second and first order transition lines. The exponents of the low temperature asymptotics at the phase transitions are determined. *