We study the ground-state phase diagram of a Heisenberg model with spin S = 1 2 on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ between the length of the diagonal bond and that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn 85, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of λ c < λ < 2, are identical to the square-lattice dimer covering states, which ignited renewed interest in high-dimensional diamond-like decorated lattices. In order to determine the phase boundary λ c , we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain λ c = 0.974. Our obtained magnetizations for spin-1 2 sites and for spin-1 sites are m = 0.398 andm = 0.949, and spin reductions are 20 % and 5%, respectively. This indicates that spin fluctuation is much smaller than that of the S = 1 2 square-lattice antiferromagnet: thus, we can consider that our obtained ground-state energy is highly accurate. Further, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram. IntroductionThe exploration of frustration in quantum spin models has been one of the most interesting issues in condensed matter physics. 1 The systems consisting of diamond units with frustration have also attracted wide attention both experimentally and theoretically. 2-10The diamond chain is one of the typical systems with diamond units, and it was proposed by Takano et al. 2 It is a one-dimensional lattice system, and a diamond unit has two types of antiferromagnetic interactions. As shown in Fig. 1 (a), solid and dashed lines, respectively, represent exchange parameters J and J ′ , and the ratio λ = J ′ /J determines the ground-state properties. It has been known that, in the case of spin J. Phys. Soc. Jpn. DRAFT S = 1 2 , three types of ground-state phases exist: the dimer-monomer (DM) state for 2 < λ, the tetramer-dimer (TD) state for 0.909 < λ < 2, and the ferrimagnetic state for λ < 0.909. 2 In the TD state, as shown in Fig. 1 (a), diamond units with triplet pairs (shaded blue ovals) and with singlet pairs (unshaded red ovals) are arranged alternately. This arrangement results from the fact that for λ < 2, the energy decreases as the number of triplet pairs increases, but nearest-neighbor repulsion exists between two diamond units with triplet pairs, which can be explained by the variational principle and the Lieb-Mattice theorem. 2, 3 In the TD state, the edge spins, which are represented by the small open circles in Fig. 1 (a), always belong to a tetramer. Furthermore, as we will show later, the singlet pair on the dotted lines makes the four interactions J in the diamond unit vanish effectively. We note that the above-mentioned property of a tetramer is that of a dimer in the dimer covering model. If we regard a tetramer as a "dimer", we can ident...

We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.

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Magnetizations of ferro-and antiferromagnetic Ising models with frustration on diamond hierarchical lattices are exactly obtained at zero temperature. For the zero-field classical spin-liquid phase found in [Kobayashi et al, J. Phys. Soc. Jpn. 78, 074004 (2009) ], for which frustrating interactions play an important role, an infinitely small applied magnetic field can induce an infinitely small magnetization, despite classical Ising models that have discrete energy levels. In antiferromagnetic systems, the magnetization cannot saturate under finite magnetic fields owing to the competition between the unfrustrating antiferromagnetic interaction and the Zeeman interaction and an intrinsic long-range nature of hierarchical lattices.