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 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.
Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic
S=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.
Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}{J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at
TN into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at
TKT, which respectively occur for the Ising-type ($\mathrm{\ensuremath{\Delta}}>1$) and XY-type ($\mathrm{\ensuremath{\Delta}}<1$) anisotropies, while for the isotropic Heisenberg case of $\mathrm{\ensuremath{\Delta}}=1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the XY-type anisotropy, the longitudinal spin-current conductivity ${\ensuremath{\sigma}}_{xx}^{s}$ ($={\ensuremath{\sigma}}_{yy}^{s}$) exhibits a divergence at
TKT of the exponential form ${\ensuremath{\sigma}}_{xx}^{s}\ensuremath{\propto}exp\left[B/\sqrt{T/{T}_{\text{KT}}\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\right]$ with
B=O(1), while for the Ising-type anisotropy, the temperature dependence of ${\ensuremath{\sigma}}_{xx}^{s}$ is almost monotonic without showing a clear anomaly at
TN and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\ensuremath{\sigma}}_{xx}^{s}$ at
TKT is found to be due to the exponential rapid growth of the spin-current relaxation time toward
TKT, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward
TKT. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.
An anisotropic Heisenberg spin S = 1 model on a two-dimensional hexagonal lattice (formed from interacting chains) with antiferromagnetic nearest-neighbor interactions of two types is analyzed by the real space renormalization group method. The problem of the influence of interchain pairing on the critical properties of the model is studied, and the phase diagram of the model is constructed. The two-dimensional density matrix renormalization group algorithm is used to calculate the ground state energy for the isotropic case as a function of the ratio between interchain and intrachain interactions.