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Register a new userInvestigation of entanglement measures across the magnetization process of a highly frustrated spin-1/2 Heisenberg octahedral chain as a new paradigm of the localized-magnon approach
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The bipartite entanglement across the magnetization process of a highly frustrated spin-1/2 Heisenberg octahedral chain is examined within the concept of localized magnons, which enables a simple calculation of the concurrence measuring a strength of the pairwise entanglement between nearest-neighbor and next-nearest-neighbor spins from square plaquettes. A full exact diagonalization of the finite-size Heisenberg octahedral chain with up to 4 unit cells (20 spins) evidences an extraordinary high precision of the localized-magnon theory in predicting measures of the bipartite entanglement at sufficiently low temperatures. While the monomer-tetramer phase emergent at low enough magnetic fields exhibits presence (absence) of the bipartite entanglement between the nearest-neighbor (next-nearest-neighbor) spins, the magnon-crystal phase emergent below the saturation field contrarily displays identical bipartite entanglement between the nearest-neighbor and next-nearest-neighbor spins. The presented results verify a new paradigm of the localized-magnon approach concerned with a simple calculation of entanglement measures.
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The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is investigated using variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The investigated model has in a magnetic field an extraordinarily rich ground-state phase diagram, which includes the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin liquids and two bound magnon crystals in addition to the fully polarized ferromagnetic phase. The lowest-energy eigenstates in a highly-frustrated parameter region belong to flat bands and hence, low-temperature thermodynamics above the bound magnon-crystal ground states can be satisfactorily described within the localized-magnon approach. The variational method provides an exact evidence for the magnon-crystal phase with a character of the monomer-tetramer ground state at zero field, while another magnon-crystal phase with a single bound magnon at each square plaquette is found in a high-field region. A diversity of quantum ground states gives rise to manifold zero-temperature magnetization curves, which may involve up to four wide intermediate plateaus at zero, one-sixth, one-third and two-thirds of the saturation magnetization, two quantum spin-liquid regions and two tiny plateaus at one-ninth and one-twelfth of the saturation magnetization corresponding to the fragmentized cluster-based Haldane phases.
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at a half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs which are absent in the Ising-Heisenberg counterpart model.
A full energy spectrum of the spin-1/2 Heisenberg cubic cluster is used to investigate a low-temperature magnetization process and adiabatic demagnetization of this zero-dimensional 2x2x2 quantum spin system. It is shown that the antiferromagnetic spin-1/2 Heisenberg cube exhibits at low enough temperatures a stepwise magnetization curve with four intermediate plateaux at zero, one quarter, one half, and three quarters of the saturation magnetization. We have also found the enhanced magnetocaloric effect close to level-crossing fields that determine transitions between the intermediate plateaux.
We investigate the critical behavior of the S=1/2 alternating Heisenberg chain using the density matrix renormalization group (DMRG). The ground-state energy per spin and singlet-triplet energy gap are determined for a range of alternations. Our results for the approach of the ground-state energy to the uniform chain limit are well described by a power law with exponent p=1.45. The singlet-triplet gap is also well described by a power law, with a critical exponent of p=0.73, half of the ground-state energy exponent. The renormalization group predictions of power laws with logarithmic corrections can also accurately describe our data provided that a surprisingly large scale parameter is present in the logarithm.
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.
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