High-Field and Multifrequency ESR Studies at KYOKUGEN in Osaka University

We have developed high-field and multifrequency (HFMF) electron spin resonance (ESR) apparatus for the magnetic fields up to 65 T at frequencies up to about 6 THz. In addition to this pulsed field ESR apparatus, we are making a multifrequency ESR apparatus with very high sensitivity in a static field. We report the results of ESR studies on BaCoV₂O₈ and NiGa₂S₄, followed by recent developments and future plans of our HFMF ESR apparatus.     

Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips

We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L_x vertices and of width L_y vertices and, in the L_x→∞ limit, the exponent of the ground state entropy, W=e^S₀/k_B. The strips considered, with their boundary conditions (BC), are (a) (FBC_y, PBC_x) = cyclic for L_y=3, 4, (b) (FBC_y, TPBC_x) = Möbius, L_y=3, (c) (PBC_y, PBC_x) = toroidal, L_y=3, (d) (PBC_y, TPBC_x) = Klein bottle, L_y=3, (e) (PBC_y, FBC_x) = cylindrical, L_y=5, 6, and (f) (FBC_y, FBC_x) = free, L_y=5, where F, P, and TP denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2πL_x/3) for case (c). The continuous locus of points where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices.     

二维三角光学格子中的PT光孤子研究

研究了基于自散焦克尔非线性的PT对称三角格子中双峰光孤子的存在性及稳定性。采用改进的平方算子法(MSOM)迭代计算出孤子的数值解,发现双峰之间具有相同相位的双峰光孤子存在于第一带隙,并且可以在某个范围内稳定传输。由傅里叶配点法得到的线性稳定性与非线性模拟传输的结果是一致的。此外,这种PT对称的双峰光孤子对入射角度非常敏感,从不同角度入射的光孤子具有不同的传输特性。     

Hidden Symmetries in the Two-Dimensional Isotropic Antiferromagnet

We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex physical system in arbitrary sequences of reference frames. All theories of the fundamental interactions rely on gauge invariance. In Dirac’s approach, the two-dimensional isotropic antiferromagnet is subject to second-class constraints, which are independent of the Hamiltonian symmetries and can be used to eliminate certain canonical variables from the theory. We have used the symplectic embedding formalism developed by a few of us to make the system under study gauge invariant. After carrying out the embedding and Dirac analysis, we systematically show how second-class constraints can generate hidden symmetries. We obtain the invariant second-order Lagrangian and the gauge-invariant model Hamiltonian. Finally, for a particular choice of factor ordering, we derive the functional Schröodinger equations for the original Hamiltonian and for the first-class Hamiltonian and show them to be identical, which justifies our choice of factor ordering.     

Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice

The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality \(\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d\). Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.     

Theory of Photo-emission from the Two-Dimensional t-J Model on a Triangular Lattice

The electron spectral function, the electron dispersion, and the electron density of states of the two-dimensional t-J model on a triangular lattice are studied within the selfconsistent fermion-spin mean-field theory. It is shown that there is a gap in the electron dispersions, and the global features of the electron spectral function is qualitatively similar to the result of the t-J model on a square lattice.     

Spin disorder and order in quasi-2D triangular Heisenberg antiferromagnets: comparative study of FeGa2S4, Fe2Ga2S5, and NiGa2S4

Our single crystal study reveals that the single-layer S=2 triangular Heisenberg antiferromagnet FeGa2S4 forms a frozen spin-disordered state, similar to the S=1 isostructural magnet NiGa2S4. In this state, the magnetic specific heat C{M} is not only insensitive to the field, but shows a T2 dependence that scales to C{M} of NiGa2S4, suggesting the same underlying mechanism of the 2D coherent behavior. In contrast, the bilayer system Fe2Ga2S5 exhibits a 3D antiferromagnetic order.     

Microscopic Theory of the Two-Dimensional Quantum Antiferromagnet in a Paramagnetic Phase

We have developed a consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with a short range antiferromagnetic order on the basis of the path integral for spin coherent states. In the framework of our approach we have obtained the response function for the spin fluctuations for all values of the frequency ω and the wave vector k and have calculated the free energy of the system. We have also reproduced the known results for the spin correlation length in the lowest order in 1/N. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and found natural variables in terms of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to those in the spin wave theory and they are on the order of the smallness parameter 1/2s where s is the spin magnitude. The long-wave spin fluctuations are governed by the nonlinear sigma model and are on the order of the smallness parameter 1/N, where N is the number of field components. We also have shown that the short wave spin fluctuations must be evaluated accurately and the continuum limit in time of the path integral must be performed after the summation over the frequencies ω.     

Height Representation,Critical Exponents,and Ergodicity in the Four-State Triangular Potts Antiferromagnet

We study the four-state antiferromagnetic Potts model on the triangular lattice. We show that the model has six types of defects which diffuse and annihilate according to certain conservation laws consistent with their having a vector-valued topological charge. Using the properties of these defects, we deduce a (2+2)-dimensional height representation for the model and hence show that the model is equivalent to the three-state Potts antiferromagnet on the Kagomé lattice and to bond-coloring models on the triangular and honeycomb lattices. We also calculate critical exponents for the ground-state ensemble of the model. We find that the exponents governing the spin–spin correlation function and spin fluctuations violate the Fisher scaling law because of constraints on path length which increase the effective wavelength of the spin operator on the height lattice. We confirm our predictions by extensive Monte Carlo simulations of the model using the Wang–Swendsen–Kotecký cluster algorithm. Although this algorithm is not ergodic on lattices with toroidal boundary conditions, we prove that it is ergodic on lattices whose topology has no noncontractible loops of infinite order, such as the projective plane. To guard against biases introduced by lack of ergodicity, we perform our simulations on both the torus and the projective plane.     

太赫兹波段三角晶格二维光子晶体的传输特性

用平面波展开法研究了太赫兹(THz)波在二维三角晶格光子晶体中的传输特性。数值计算了以硅为背景的空气圆柱构成的二维三角晶格光子晶体的能带结构和态密度,计算表明在介质圆柱半径r=0.47a(a为空气介质柱的晶格常数)出现最大完全光子带隙,带隙宽度为0.070 1 THz;当r=0.49a和r=0.45a时,E偏振和H偏振分别出现最大光子带隙,带隙宽度分别0.102 2,0.192 3 THz。光子晶体能态密度的分布也表明了存在光子带隙的范围。研究结果为THz器件的开发提供了理论依据。     

Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.     

Classical Density Functional Theory Approach to the Vibrational Properties and Lattice Specific Heat of a Quasi-One-Dimensional Antiferromagnet KFeSe2

JETP Letters - We have performed ab initio calculations of vibrational properties of KFeSe2 compound utilizing density functional theory. Total and element specific phonon densities of states have...     

Decomposition of the Fock Space in Two-Dimensional Square Lattice Systems

We discuss how to decompose the Fock space of a many-fermion system embedded in two-dimensional square lattice. Wefirst notice that the symmetry group inherent in the system is one of the two-dimensional space groups. We shortly review thecorresponding irreducible representations of the group. We then find the characters of the reducible representation of the many-fermion Fock space. Using the characters, we obtain the multiplicity of each irreducible representation contained in the Fock space of a fixed number of fermions. We present specific examples, where we calculate the multiplicities which are the dimensions of the decomposed spaces.