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Observation of a quantum spin liquid (QSL) state is one of the most important goals in condensed-matter physics, as well as the development of new spintronic devices that support next-generation industries. The QSL in two dimensional quantum spin systems is expected to be due to geometrical magnetic frustration, and thus a kagome-based lattice is the most probable playground for QSL. Here, we report the first experimental results of the QSL state on a square-kagome quantum antiferromagnet, KCu6AlBiO4(SO4)5Cl. Comprehensive experimental studies via magnetic susceptibility, magnetisation, heat capacity, muon spin relaxation (μSR), and inelastic neutron scattering (INS) measurements reveal the formation of a gapless QSL at very low temperatures close to the ground state. The QSL behavior cannot be explained fully by a frustrated Heisenberg model with nearest-neighbor exchange interactions, providing a theoretical challenge to unveil the nature of the QSL state., 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.

Highly frustrated spin systems such as the kagome lattice are a treasure trove of new quantum states with large entanglements. Herein, we study the spin-$$\frac{1}{2}$$ 1 2 Heisenberg model on a kagome-strip chain, which is a one-dimensional kagome lattice, using the density matrix renormalization group method. Calculating the central charge and entanglement spectrum for the kagome-strip chain, we find a gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated using the dynamical density matrix renormalization group method. We then propose a resonating dimer–monomer liquid state that meets these features.

Recent experimental study on Tsai-type quasicrystalline approximant Au-Al-Gd has revealed the presence of magnetic orders and phase transitions with changing the Au/Al concentration. Motivated by the experiment, we theoretically investigate whether a successive change of magnetic orders occurs in a minimal magnetic model including the RKKY interaction only. We find that the model induces multifarious magnetic orders depending on the Fermi wavenumber and gives a good starting point for understanding the experimental observation. In addition, we predict the presence of an undiscovered novel magnetic order called cuboc order at large Fermi wavenumber region., 6 pages, 4 figures

The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds ${A}_{2}{\mathrm{CoTeO}}_{6}$ ($A=\text{Ca}$, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in the model, indicating the possibility to observe supersolid phases in these compounds. We also find that one of the supersolid phases is similar to the nonclassical coplanar phase obtained in the $XXZ$ model on the triangular lattice.

The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study of how the phases in the two lattices merge with each other when geometry changes from the honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a ground state phase diagram of this model with classical spins by using the Luttinger-Tisza method and classical Monte Carlo simulation. In addition to known phases in the honeycomb and triangular lattices, we find coexisting phases consisting of the known phases. From the exact diagonalization and density-matrix renormalization-group calculations for the model with quantum spins, we find phases similar to the classical results, implying a small effect of quantum fluctuation on the phase diagram.

The Kitaev-Heisenberg model on the honeycomb lattice has been studied for the purpose of finding exotic states such as quantum spin liquid and topological orders. On the kagome lattice, in spite of a spin-liquid ground state in the Heisenberg model, the stability of the spin-liquid state has hardly been studied in the presence of the Kitaev interaction. Therefore, we investigate the ground state of the classical and quantum spin systems of the kagome Kitaev-Heisenberg model. In the classical system, we obtain an exact phase diagram that has an eightfold degenerated canted ferromagnetic phase and a subextensive degenerated Kitaev antiferromagnetic phase. In the quantum system, using Lanczos-type exact diagonalization and cluster mean-field methods, we obtain two quantum spin-liquid phases, an eightfold degenerated canted ferromagnetic phase similar to the classical spin system, and an eightfold degenerated, $\mathbf{q}=\mathbf{0},{120}^{\ensuremath{\circ}}$ ordered phase induced by quantum fluctuation. These results may provide a crucial clue to recently observed magnetic structures of the rare-earth-based kagome lattice compounds ${A}_{2}{\mathrm{RE}}_{3}{\mathrm{Sb}}_{3}{\mathrm{O}}_{14}\phantom{\rule{4pt}{0ex}}(A=\text{Mg}$, Zn; $\text{RE}=\text{Pr}$, Nd, Gd, Tb, Dy, Ho, Er, Yb).

K3Cu3AlO2(SO4)4 is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90 mK, which is roughly three orders of magnitude lower than the exchange interaction of the quantum AFM chain. K3Cu3AlO2(SO4)4 is, thus, regarded as a compound that exhibits a Tomonaga-Luttinger spin liquid behavior at low temperatures close to the ground state.

The spin-$\frac{1}{2}$ 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-$\frac{1}{2}$ 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.

Spin-$\frac{1}{2}$ compounds ${A}_{3}{\mathrm{Cu}}_{3}{\mathrm{AlO}}_{2}{({\mathrm{SO}}_{4})}_{4}\phantom{\rule{0.28em}{0ex}}(A=\mathrm{K},\phantom{\rule{0.28em}{0ex}}\mathrm{Rb},\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}\mathrm{Cs})$ have one-dimensional (1D) inequilateral diamond chains. We analyze the temperature dependence of the magnetic susceptibility and determine the magnetic exchange interactions. In contrast to azurite, a dimer is formed on one of the sides of the diamond. From numerical analyses of the proposed model, we find that the dimer together with a nearly isolated 1D Heisenberg chain characterize magnetic properties including magnetization curve and magnetic excitations. This implies that a dimer-monomer composite chain without frustration is a good starting point for describing these compounds.

We study the ground state of the $S=\frac{1}{2}$ 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 $M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}$, and $\frac{3}{4}$, where ${M}_{\mathrm{sat}}$ is the saturated magnetization. The obtained $\frac{3}{4}$ plateau state is consistent with the exact result, and the $\frac{1}{2}$ plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the $\frac{1}{3}$ plateau of the kagome lattice. Different four-spin loop structures are obtained in the $\frac{1}{4}$ and $\frac{3}{8}$ plateaus but no corresponding states exist in the kagome lattice. The $\frac{3}{8}$ plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

We study the magnetic field dependence of the ground state of the S = 1/2 J1–J2 Heisenberg model on the square lattice by the density matrix renormalization group (DMRG) method. With the use of the sine-square deformation, we obtain eight different ground states including plaquette valence-bond crystal with a finite spin gap, transverse Neel, transverse stripe, 1/2 magnetization plateau with up–up–up–down (uuud), and three new states we named the Y-like, V-like, and Ψ states around J2/J1 = 0.55–0.6. The phase transitions from the transverse Neel (at J2/J1 = 0.55) and stripe (at J2/J1 = 0.6) states to the uuud and Y-like states, respectively, are discontinuous, as in the case of a spin flop.

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.

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 system. Residual entropy is in a range of 0~6.1% of the entropy at high temperature for hexagonal diamond lattice and 0~8.4% for square diamond lattice. These diamond lattices are generalized to any dimensions and it is likely to be synthesized experimentally., Comment: 4 pages, 5 figures