We consider the strongly anisotropic spin-1/2 $XXZ$ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction $J^{zz}=Delta J$ and aniferromagnetic transversal interaction $J^{xx}=J^{yy}=J>0$. At $Delta=-1/2$ the lowest one-magn
on excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.~J.~Changlani et at., Phys. Rev. Lett. {bf 120}, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations.
The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys. Ges. {bf 2}, 202-2
04 (1900)] we calculate thermodynamic properties of this model by interpolating between the low- and high-temperature behavior. For that we follow ideas developed in detail by B.~Bernu and G.~Misguich and use for the interpolation the entropy exploiting sum rules [the ``entropy method (EM)]. We complement the EM results for the specific heat, the entropy, and the susceptibility by corresponding results obtained by the finite-temperature Lanczos method (FTLM) for a finite lattice of $N=32$ sites as well as by the high-temperature expansion (HTE) data. We find that due to pronounced finite-size effects the FTLM data for $N=32$ are not representative for the infinite system below $T approx 0.7$. A similar restriction to $T gtrsim 0.7$ holds for the HTE designed for the infinite PHAF. By contrast, the EM provides reliable data for the whole temperature region for the infinite PHAF. We find evidence for a gapless spectrum leading to a power-law behavior of the specific heat at low $T$ and for a single maximum in $c(T)$ at $Tapprox 0.25$. For the susceptibility $chi(T)$ we find indications of a monotonous increase of $chi$ upon decreasing of $T$ reaching $chi_0 approx 0.1$ at $T=0$. Moreover, the EM allows to estimate the ground-state energy to $e_0approx -0.52$.
Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$frac{1}{2}$ isotropic ($XXX$)
Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this q
uantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop like transition in the considered isotropic spin model.
We consider a geometrically frustrated spin-1/2 Ising-Heisenberg diamond chain, which is an exactly solvable model when assuming part of the exchange interactions as Heisenberg ones and another part as Ising ones. A small $XY$ part is afterwards pert
urbatively added to the Ising couplings, which enabled us to derive an effective Hamiltonian describing the low-energy behavior of the modified but full quantum version of the initial model. The effective model is much simpler and free of frustration. It is shown that the $XY$ part added to the originally Ising interaction gives rise to the spin-liquid phase with continuously varying magnetization, which emerges in between the magnetization plateaus and is totally absent in the initial hybrid diamond-chain model. The elaborated approach can also be applied to other hybrid Ising-Heisenberg spin systems.
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau
states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
