Magnetic properties of the spin S=1/2S=1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange %on even and odd sites in the presence of additional modulation of exchange on odd bonds with period three. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective $XXZ$ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped string order into the only one gapless L\"uttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to 1/3 and 2/3 of the saturation value. These phases reveal themselves also in magnetization curve as plateaus at corresponding values of magnetization. As the result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.Comment: 21 pages, 5 figures, Journal of Physics: Condensed Matter, 24, 116002, (2012

Magnetic phase diagram of the dimerized spin S=1/2S=1/2 ladder

The ground-state magnetic phase diagram of a spin $S=1/2$ two-leg ladder with alternating rung exchange $J_{\perp}(n)=J_{\perp}[1 + (-1)^{n} \delta]$ is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N=28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as $\delta^{\nu}$, where critical exponent varies from $\nu =0.87\pm0.01$ in the case of a ladder with isotropic antiferromagnetic legs to $\nu =1.82\pm0.01$ in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:cond-mat/0603153, arXiv:1110.446

Entanglement and quantum correlations in the XX spin-1/21/2 honeycomb lattice

The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the N\'eel and the dimerized phases have been identified. Moreover, canted N\'eel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two complementary numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a "magnetic-entanglement" behavior that starts from an entangled field around the saturation field.Comment: 8 pages, 5 figure

Violating Bell inequality using weak coherent states

We present an experimental investigation of two-photon interference using a continuous-wave laser. We demonstrate the violation of the CHSH inequality using the phase randomized weak coherent states from a continuous wave laser. Our implementation serves as an approach to reveal the quantum nature of a source that is considered to be a classical source.Comment: 6 pages, 2 figure