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The kagome lattice is an ideal platform for studying the effects of frustration in spin systems. Here, the authors investigate a half-integer spin chain placed on a one-dimensional kagome system finding a rich phase diagram that presents a gapless spin-liquid phase and supports their results through a resonating dimer–monomer model

There exist many theoretical models of frustrated quantum magnetism, most of which lack convincing experimental realisations. Here the authors combine several experimental methods to argue that KCu6AlBiO4(SO4)5Cl behaves as a square-kagome-lattice quantum Heisenberg antiferromagnet.

The Haldane state is a typical quantum and topological state of matter, which exhibits an edge state corresponding to symmetry-protected topological order in a one-dimensional integer spin chain. Here we propose a concept to design the Haldane state with one-half spins by making use of a chain composed of one-half spin clusters. If the clusters contain two spins, the ground state of a chain corresponds to the Affleck-Kennedy-Lieb-Tasaki state. We thus extend this knowledge to general clusters consisting of not only even, but odd numbers of one-half spins. In the case of an odd number of spins in the clusters, we present a concrete procedure to construct a field-induced Haldane state, and demonstrate the Haldane state in a five-spin cluster chain. Our concept is useful to understand quantum magnetism in real materials such as Fedotovite, consisting of six-spin clusters aligned in one dimension. Furthermore, the edge state designed by our flexible scheme can be utilized for a processing unit of quantum computation with recent progress on intended synthesis of organic materials, quantum dots, and optical lattices.

Frustrated quantum spin systems such as the Heisenberg and Kitaev models on various lattices have been known to exhibit various exotic properties not only at zero temperature but also for finite temperatures. Inspired by the remarkable development of the quantum frustrated spin systems in recent years, we investigate the finite-temperature properties of the S=1/2 Kitaev-Heisenberg models on kagome and triangular lattices by means of finite-temperature Lanczos methods with improved accuracy. In both lattices, multiple peaks are confirmed in the specific heat. To find the origin of the multiple peaks, we calculate the static spin structure factor. The origin of the high-temperature peak of the specific heat is attributed to a crossover from the paramagnetic state to a short-range ordered state whose static spin structure factor has zigzag or linear intensity distributions in momentum space. In the triangular Kitaev model, the “order by disorder” due to quantum fluctuation occurs. On the other hand, in the kagome Kitaev model it does not occur even with both quantum and thermal fluctuations.

The magnetic diffuse scattering of YBaCo4O7 and LuBaCo4O7 with alternating kagome and triangular lattices has been studied through neutron scattering measurements on single-crystal samples. In YBaCo4O7, the line-shapemagnetic-diffuse scattering is observed around the magnetic transition temperature, which is consistent with the Monte Carlo simulation. In LuBaCo4O7, the line-shape-magnetic-diffuse scattering has not been detected. At low temperature, the propagation vectors of the observed magnetic reflections are different between YBaCo4O7 and LuBaCo4O7. The structural distortion in RBaCo4O7 is suggested to play a critical role for the magnetic properties [ABSTRACT FROM AUTHOR]

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1=2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1=3 and 2=3 plateaus in the model with two equivalent bonds, we find a new 2=3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one. [ABSTRACT FROM AUTHOR]

Exactly solvable frustrated quantum spin models consisting of a diamond unit structure are presented. The ground states are characterized by tetramer-dimer states with a macroscopic degeneracy in a certain range of isotropic exchange interaction. The lower bound of the excitation gap is exactly calculated to be finite, and the bulk entropy in the limit of zero temperature remains finite depending on the shape of the boundary of the system. Residual entropy is in the range of 0-6.1% of the entropy at high temperature for a hexagonal diamond lattice and 0-8.4% for a square diamond lattice. These diamond spin lattices are generalized to any dimensions and some of them are likely to be synthesized experimentally. [ABSTRACT FROM AUTHOR]

The spin- 1/2 Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin- 1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells. [ABSTRACT FROM AUTHOR]

We study the ground state of the S=1/2 Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at M/Msat=0,1/4,3/8,1/2, and 3/4, where Msat is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a 4√2 ?2√2 magnetic unit cell with a 16-fold degeneracy. [ABSTRACT FROM AUTHOR]