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arXiv:0907.4168 · Journal of Physics Conference Series

Quantum Heisenberg antiferromagnetic chains with exchange and single-ion anisotropies

D Peters, Ian P. McCulloch, Walter Selke

Published Jan 1, 2010• 11 citations
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Abstract

Using density matrix renormalization group calculations, ground state properties of the spin–1 Heisenberg chain with exchange and quadratic single-ion anisotropies in an external field are studied, for special choices of the two kinds of anisotropies. In particular, the phase diagram includes antiferromagnetic, spin-liquid (or spin-flop), IS2, and supersolid (or biconical) phases. Especially, new features of the spin-liquid and supersolid phases are discussed. Properties of the quantum chains are compared to those of corresponding classical spin chains.

DOI
10.1088/1742-6596/200/2/022046

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Using density matrix renormalization group calculations, ground state properties of the spin–1 Heisenberg chain with exchange and quadratic single-ion anisotropies in an external field are studied, for special choices of the two kinds of anisotropies. In particular, the phase diagram includes antiferromagnetic, spin-liquid (or spin-flop), IS2, and supersolid (or biconical) phases. Especially, new features of the spin-liquid and supersolid phases are discussed. Properties of the quantum chains are compared to those of corresponding classical spin chains.
Using density-matrix renormalization group calculations, ground-state properties of the spin-1 Heisenberg chain with exchange and single-ion anisotropies in an external field are studied. Our findings confirm and refine recent numerical and analytic results by Sengupta and Batista [Phys. Rev. Lett. 99, 217205 (2007)] on the same model. In particular, we present evidence for two types of biconical (or supersolid) and for two types of spin-flop (or superfluid) structures for chains of finite length. Basic features of the quantum phase diagram may be interpreted qualitatively in the framework of classical spin models.
We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field.The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases.Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed.Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic S=1S=1S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.
We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.