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Register a new userFrustrated spin-$frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_{1}$--$J_{2}$--$J_{1}^{perp}$ model
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The zero-temperature phase diagram of the spin-$frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} equiv kappa J_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{perp} equiv delta J_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the N{e}el or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $delta < 0$) or antiparallel (when $delta > 0$) to one another. Calculations are performed at $n$th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with $n leq 10$. The sole approximation made is to extrapolate such sequences of $n$th-order results for $M$ to the exact limit, $n to infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $kappa$--$delta$ half-plane with $kappa > 0$. In particular, we provide the accurate estimate, ($kappa approx 0.547,delta approx -0.45$), for the position of the quantum triple point (QTP) in the region $delta < 0$. We also show that there is no counterpart of such a QTP in the region $delta > 0$, where the two quasiclassical phase boundaries show instead an ``avoided crossing behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected.
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The zero-temperature quantum phase diagram of the spin-$frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{perp}$ model on an $AA$-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} equiv kappa J_{1}>0$. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_{1}^{perp} equiv delta J_{1}$. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the N{e}el and N{e}el-II phases, are calculated in the $kappa delta$ half-plane with $kappa > 0$. Whereas on each monolayer in the N{e}el state all NN pairs of spins are antiparallel, in the N{e}el-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter $M$ and the excitation energy $Delta$ from the $s^{z}_{T}=0$ ground state to the lowest-lying $|s^{z}_{T}|=1$ excited state (where $s^{z}_{T}$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders ($n leq 10$) in a systematic series of approximations involving $n$-spin clusters. The sole approximation made is then to extrapolate the sequences of $n$th-order results for $M$ and $Delta$ to the exact limit, $n to infty$.
We study a frustrated 3D antiferromagnet of stacked $J_1 - J_2$ layers. The intermediate quantum spin liquid phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this there is a direct first-order transition from N{ e}el to columnar order. Possible applications to real materials are discussed.
Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range magnetic order are found down to 0.3~K, evidencing a highly frustrated spin-liquid-like ground state in zero field. Above 2,T, signatures of magnetic order are observed in thermodynamic measurements, suggesting the possibility of a field-induced quantum phase transition. The $^{23}$Na NMR relaxation rates reveal the absence of magnetic order and persistent fluctuations down to 0.3~K at very low fields and confirm the bulk magnetic order above 2~T. The $H$-$T$ phase diagram is obtained and discussed along with the existing theoretical concepts for layered spin-$frac{1}{2}$ triangular-lattice antiferromagnets
We theoretically investigate, within the Schwinger-Boson mean-field theory, the transition from a gapped $Z_{2}$ quantum spin-liquid, in a $J_1$-$J_2$ Heisenberg spin-1/2 system in a honeycomb lattice, to a chiral $Z_2$ spin liquid phase under the presence of time-reversal symmetry breaking scalar chiral interaction (with amplitude $J_{chi}$), with non-trivial Chern bands of the excitations. We numerically obtain a phase diagram of such $J_1$-$J_2$-$J_{chi}$ system, where different phases are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation and the symmetries of the mean-field parameters. The chiral $Z_2$ state is characterized by non-trivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to large thermal Hall coefficient.
We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Greens function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are more efficient in the pyrochlore case (finite-temperature frustration effects). Our results may be of use for interpreting experimental data for ferromagnetic pyrochlore materials.
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