Global Quantum Correlation in the Ising model

We study quantum correlations in an isotropic Ising ring under the effects of a transverse magnetic field. After characterizing the behavior of two-spin quantum correlations, we extend our analysis to global properties of the ring, using a figure of merit for quantum correlations that shows enough sensitivity to reveal the drastic changes in the properties of the system at criticality. This opens up the possibility to relate statistical properties of quantum many-body systems to suitably tailored measures of quantum correlations that capture features going far beyond standard quantum entanglement.Comment: Published in the International Journal of Quantum Information as part of the special issue devoted to "Quantum Correlations: entanglement and beyond

Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio

Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems

We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration examples, a one-dimensional and a two-dimensional $XY$ models are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points

Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction

We have studied occurrence of quantum phase transition in the one-dimensional spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi- partite and multi-partite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 24 qubits. The minimum of the entanglement ratio R $\equiv$ \tau 2/\tau 1 < 1, as a novel estimator of QPT, has been used to detect QPT and our calculations have shown that its minimum took place at the critical point. We have also shown both the global-entanglement (GE) and multipartite entanglement (ME) are maximal at the critical point for the Ising chain with added DM interaction. Using matrix product state approach, we have calculated the tangle and concurrence of the model and it is able to capture and confirm our numerical experiment result. Lack of inversion symmetry in the presence of DM interaction stimulated us to study entanglement of three qubits in symmetric and antisymmetric way which brings some surprising results.Comment: 18 pages, 9 figures, submitte

Entanglement in extended Hubbard models and quantum phase transitions

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.Comment: 14 pages, 8 figures, 2 table

Genuine correlations in finite-size spin systems

Genuine multipartite correlations in finite-size XY chains are studied as a function of the applied external magnetic field. We find that, for low temperatures, multipartite correlations are sensitive to the parity change in the Hamiltonian ground state, given that they exhibit a minimum every time that the ground state becomes degenerate. This implies that they can be used to detect the factorizing point, that is, the value of the external field such that, in the termodynamical limit, the ground state becomes the tensor product of single-spin states.Comment: Submitted to Int. J. Mod. Phys. B, special issue "Classical Vs Quantum correlations in composite systems" edited by L. Amico, S. Bose, V. Korepin and V. Vedra