Multiple electron self-injection in laser wake-field acceleration is studied via fully relativistic two- and three-dimensional particle-in-cell simulation. The electron density modulation in the laser wake originating from oscillations of the laser pulse waist and relativistic effects can provoke the parametric resonance in the electron fluid momentum. This may result in repetitive trapping of plasma electrons in the acceleration phase of the laser wake: multiple electron self-injection. The maximal energy of the accelerated electrons depends strongly on the total charge of the injected electrons. A low energy spread, less than 1%, for an almost 1GeV energy electron beam with charge about 10pC is found numerically in the plasma channel irradiated by a 25TW laser pulse, while a 200TW laser pulse produces a few nC beam with only 150MeV energy. Essentially thermalization of accelerated electrons is also a result of charge loading.

The magnetization process in the Shastry-Sutherland system is studied by using the thirdorder perturbation expansion. It is shown that the 1/3-plateau is realized by the second-order perturbation, which is not prevented by the off-diagonal part. In each subspace whose magnetization per dimer is less than 1/3, the lowest energy state is determined by a small but finite energy-gain due to the third-order correlated flip terms and there exists no plateau originating from the third-order effect. Our results are compared with those of the exact diagonalization method to discuss the validity of truncation of states in our perturbation theory.In the last couple of years there has been a growing interest in the phenomenon of magnetization plateaus in two-dimensional spin systems. For instance, the existence of plateaus in the magnetization curve is theoretically shown in the multiple-spin exchange model on the triangular lattice 1) and the Heisenberg antiferromagnet on the 1/5-depleted square lattice. 2) As for the experimental investigations of this phenomenon, recently, Kageyama et al. measured the magnetization curve of SrCu 2 (BO 3 ) 2 up to the magnetic field H = 45 T and observed intermediate plateaus at 1/8 (for 27.9 < H < 29.8 T) and 1/4 (for 37.0 < H < 41.0 T) of the full Cu moment. 3) In this compound, magnetic ions Cu 2+ (S = 1/2) are arranged as shown in Fig. 1.As a model for this system, Miyahara and Ueda 4) proposed a Heisenberg antiferromagnet with nearest neighbor (NN) and next nearest neighbor (NNN) couplings:which is equivalent to a model with the exact dimer ground state (for J <∼ 0.7J) proposed by Shastry and Sutherland. 5) It is reported that experimental data of the uniform susceptibility are reproduced by this model with J 100 K and J 68 K, where the exact diagonalization method is employed. 4) Another estimation J 83 K and J 55 K is obtained on the basis of the theoretical calculations of the spin gap and the susceptibility by the dimer expansion, where the disconnected dimer model defined by the first term in eq. (1) is taken as an unperturbed part and the interdimer coupling in the second term is taken as a perturbation. 6, 7)The existence of the exact dimer ground state in the present model stems from a symmetric relation in the interdimer coupling as pointed out in ref. 4. This leads to other interesting properties: an almost dispersionless triplet excitation spectrum 4) and the experimental observation of the second lowest band of triplet excitations. 8) It is natural to expect that the observed magnetization plateaus in SrCu 2 (BO 3 ) 2 originate from the symmetric properties of the interdimer coupling. 4) We now turn to the study of the magnetization process. At first we present the magnetization curves for the clusters composed of 8 ( √ 8 × √ 8), 10 ( √ 10 × √ 10) and 12 ( √ 8 × √ 18) dimers in Fig. 2, where we choose J /J(≡ λ) = 0.35. We find considerable system size dependence in the magnetization curves especially for M ≤ M s /2, where M s represents the saturation value of the magnetiz...

A frustrated Ising model on a diamond hierarchical lattice is studied. We obtain the exact partition function of this model and calculate the transition temperature, specific heat, entropy, magnetization, and ferromagnetic correlation function. Depending on the magnitude of a parameter giving the frustration, there exist three types of ground states: ferromagnetic, classical spin-liquid with highly developed short-range order, and paramagnetic. The dependence of the zero-temperature entropy on the frustration parameter has an infinite number of steps. The temperature dependence of the specific heat exhibits many peaks with decreasing temperature and entropy loss. The dominant spin configurations at low temperatures are also specified.KEYWORDS: classical spin-liquid ground state, frustration, diamond hierarchical lattice, Ising model, phase transition IntroductionMany magnetic systems with competing interactions exhibit frustration that leads to multiple ground states called spin glass or spin liquid even at the classical level. These interesting properties are attributable to the delicate balance of frustrated spin-spin interactions. If we can obtain the exact partition function of a model with frustrated magnetic phenomena, we can obtain a better understanding of complicated frustrated phenomena.In statistical physics, few exactly soluble models with phase transitions are known, such as two-dimensional Ising model, 1 eight-vertex model, 2 one-dimensional van der Waals gas model, 3 and a hierarchical model. 4 Since Berker and Ostlund proposed a hierarchical model related to the renormalization group method, 4, 5 many different models on hierarchical lattices have been proposed and developed.5-8 The magnetic and thermodynamic behaviors have been studied, 9-11 and the distribution of the zeros of the partition function and the critical exponents have also been obtained.10, 12 Using a hierarchical model with competing ferro-and antiferromagnetic interactions, McKay et al. studied the spin-glass behavior 13 and Nogueria et al. investigated the local magnetization.14 However, to the best of our knowledge, no hierarchical model describes the spin-liquid ground state. In this study, we consider a hierarchical Ising model with frustrated interactions that lead to the classical spinliquid ground state. This paper is organized as follows. We introduce our diamond hierarchical lattice and frustrated Ising model in §2 and describe our recursion relations in §3. Thermodynamic and ground state properties are described in §4 and §5, respectively. In §6, the temperature evolution of dominant spin configurations at low temperatures is discussed. In §7, we summarize the results obtained in this study.

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.