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 consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.

We extend the program initiated in [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.

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin [14] for domain wall boundary conditions, we examine some modifications of these boundary conditions. To be precise, we discuss partial domain wall boundary conditions, reflecting ends and half turn boundary conditions (domain wall boundary conditions with half turn symmetry). arXiv:1711.07905v2 [cond-mat.stat-mech] 9 May 2018

We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain inhomogeneous rational vertex models combining bosonic and spin representations of SU (2), subject to non-diagonal toroidal and open boundary conditions. Only open boundary conditions are found to lead to integrable Hamiltonians combining both rotating and counter-rotating terms in the interaction. If the boundary matrices can be brought to triangular form simultaneously, the spectrum of the model can be obtained by means of the algebraic Bethe ansatz after a suitable gauge transformation; the corresponding Hamiltonians are found to be non-hermitian. Alternatively, a certain quasi-classical limit of the transfer matrix is considered where hermitian Hamiltonians are obtained as members of a family of commuting operators; their diagonalization, however, remains an unsolved problem.