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Bulletin of the American Physical Society

Bilinear-biquadratic anisotropic Heisenberg model on a triangular lattice

Antonio S. T. Pires

Published Mar 21, 2013• 0 citations
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Abstract

Abstract Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value D C , where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.

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Abstract Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value D C , where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.
The S=1S=1S=1 bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner et al., Phys. Rev. B 90, 144409 (2014)], including an extensive region of ``supersolid'' order. In this work, we amend the model by an XXZXXZXXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable S=1S=1S=1 generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZXXZXXZ anisotropy parameter, the ratio of bilinear and biquadratic interactions, and single-ion anisotropy, and we compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e., with ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1,0)$ Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing nontrivial Ising-ordered ground states.
Phase diagrams and excitations of anisotropic S=1S=1S=1 quantum magnets on the triangular lattice
The S=1S=1S=1 bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner et al.\textit{et al.}et al., Phys. Rev. B 90\textbf{90}90, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable S=1S=1S=1 generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with Sz=±1,0S^z=\pm1,0Sz=±1,0) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.
We propose a non-disordered antiferromagnetic Heisenberg spin model on a triangular lattice, which exhibits a critical state and a glassy state at low temperatures. The system has three phases, the paramagnetic, the intermediate critical, and the glassy phase. The intermediate phase is characterized by a quasi-long-range order, whereas only short-range order exists in the glassy phase. Using Monte Carlo simulation, the phase transitions and properties of the two phases at low temperatures are examined. Our spin model shows that the variable-length spin and the competition between bilinear and biquadratic interactions are essential for forming the critical and glassy phases.
Motivated by recent experiments on the material Ba3{}_{3}3​NiSb2{}_{2}2​O9{}_{9}9​, we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with d+idd+idd+id topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.
In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferromagnetic Heisenberg model of S = 1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J ⊥ c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J ⊥ c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.
The phase diagram of the anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of competitive nearest (J1)({J}_{1})(J1​)- and next-nearest $({J}_{2}=\ensuremath{\alpha}{J}_{1})$-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory in a two-spin cluster. We propose a function for the free energy, which is similar to the Landau expansion, in order to find the ground state (T=0)(T=0)(T=0) and the finite-TTT phase diagram. At zero temperature, we find a first-order quantum phase transition in the point ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta})$ between the antiferromagnetic (AF) and superantiferromagnetic (SAF) phases. This is dependent on the anisotropy parameter $\ensuremath{\Delta}$ ($\ensuremath{\Delta}=0$ and 1 correspond to the isotropic Heisenberg and Ising models, respectively). The quantum critical values of ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}\ensuremath{\ne}1)={\ensuremath{\alpha}}_{c}^{q}(\ensuremath{\Delta})$ are smaller than those of the classical model ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}=1)={\ensuremath{\alpha}}_{c}^{c}=1/4$ (for example, for $\ensuremath{\Delta}=0$, we find ${\ensuremath{\alpha}}_{c}^{q}(0)=0.21$). The former monotonically increases with the anisotropy parameter $\ensuremath{\Delta}$. The phase diagram in $T\text{\ensuremath{-}}\ensuremath{\alpha}$ plane presents a second-order transition at ${T}_{2}(\ensuremath{\alpha})$ between the AF and paramagnetic (P) phases. The phase transition between the SAF and P phases is of first-order ${T}_{1}(\ensuremath{\alpha})$ for all values of $\ensuremath{\Delta}∊[0,1]$. The phase transition lines ${T}_{1}(\ensuremath{\alpha})$ and ${T}_{2}(\ensuremath{\alpha})$ merge in a critical end point (CEP) that is dependent on $\ensuremath{\Delta}$ [i.e., ${T}_{\text{CEP}}(\ensuremath{\Delta})$ and ${\ensuremath{\alpha}}_{\text{CEP}}(\ensuremath{\Delta})$ are the temperature and frustration parameters at the CEP]. The ordered phases (AF and SAF) are separated by first-order transitions and exhibit a nontrivial re-entrant behavior at low temperatures.