Resistance Calculation of Pentagonal Lattice Structure of Resistors

In this study, the effective resistance between any two lattice sites in a two-dimensional pentagonal lattice structure of identical resistors is determined by means of the lattice Green’s function method. Some numerical results of the resistance for small separations between lattice sites are presented.     

Semiclassical ordering in the large-N pyrochlore antiferromagnet

We study the semiclassical limit of the Sp(N) generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the N --> infinity saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N = 1) semiclassical ground state.     

The expanded triangular Kitaev–Heisenberg model in the full parameter space

The classical Kitaev–Heisenberg model on the triangular lattice is investigated by simulation in its full parameter space together with the next-nearest neighboring Heisenberg interaction or the single-ion anisotropy. The variation of the system is demonstrated directly by the joint density of states (DOS) depending on energy and magnetization obtained from Wang–Landau algorithm. The Metropolis Monte Carlo simulation and the zero-temperature Glauber dynamics are performed to show the internal energy, the correlation functions and spin configurations at zero temperature. It is revealed that two types of DOS (U and inverse U) divide the whole parameter range into two main parts with antiferromagnetic and ferromagnetic features respectively. In the parameter range of U type DOS, the mixed frustration from the triangular geometry and the Kitaev interaction produces rich phases, which are influenced in different ways by the next-nearest neighboring Heisenberg interaction and the single-ion anisotropy.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.     

Quantum decoration transformation for spin models

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.     

Remarks on Perturbation of Infinite Networks of Identical Resistors

The resistance between arbitrary sites of infinite square network of identical resistors is studied when the network is perturbed by removing two bonds from the perfect lattice. A connection is made between the resistance and the lattice Green’s function of the perturbed network. By solving Dyson’s equation the Green’s function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Some numerical results are presented for an infinite square lattice.     

The anisotropic heisenberg model: High temperature series expansions in the regime of planar ordering

The procedure of Betts and coworkers, to obtain the high temperature series expansions for the XY-model is extended to the anisotropic Heisenberg model. On the f.c.c. lattice the series for the free energy and the fluctuation of the order in the XY-plane are derived up to sixth and fifth order in the inverse temperature, respectively. These series are too short to be analysed with success.     

Heisenberg对应原理下氢原子1/r矩阵元的量子-经典对应

通过详细计算表明,在准经典情况下,氢原子1r的矩阵元的量子力学结果与它的Heisenberg矩阵元近似相等,在经典极限下,它们相同. 关键词： 量子力学 对应原理     

尖晶石氧化物CoCr2O4的多铁性研究

为深入理解化合物CoCr₂O₄奇特的多铁性行为,结合尖晶石晶格结构特点,考虑近邻A-A、A-B、B-B及B位离子间次近邻交换耦合的影响,构建经典海森堡自旋模型对磁致铁电行为进行描述,并采用蒙特卡罗模拟对模型进行求解.重点考察不同磁交换耦合作用下,外磁场对体系磁化行为和电极化行为的调控.结果表明：子晶格B1离子贡献了体系的宏观磁化强度和电极化强度;近邻A-A和B位次近邻交换耦合参数的改变对子晶格A位磁性离子的磁电行为没有影响,但对B位离子的磁化强度和电极化强度有显著的调制作用,尤其是来源于子晶格B1的电极化强度对B位次近邻交换耦合参数的改变极为敏感;这些结果反映了立方尖晶石磁结构中A位和B位磁性离子环境及分布对称性的差异.     

Quantum antiferromagnetism in quasicrystals

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. Using the stochastic series expansion quantum Monte Carlo method, the distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, and a nontrivial inhomogeneous ground state is found. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. The computed spin structure factor shows antiferromagnetic modulations that can be measured in neutron scattering and nuclear magnetic resonance experiments. This generic model is a first step towards understanding magnetic quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.     

Classical antiferromagnet on a hyperkagome lattice

Motivated by recent experiments on Na4Ir3O8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This "hyperkagome" lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via "order by disorder," representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.     

Kinetic antiferromagnetism in the triangular lattice

We show that the motion of a single hole in the infinite-U Hubbard model with frustrated hopping leads to weak metallic antiferromagnetism of kinetic origin. An intimate relationship is demonstrated between the simplest versions of this problem in one and two dimensions, and two of the most subtle many body problems, namely, the Heisenberg Bethe ring in one dimension and the two-dimensional triangular lattice Heisenberg antiferromagnet.     

Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure. The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice. It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).     

Correlation inequalities for some classical spin vector models

Correlation inequalities are derived for a class of lattice systems including some classical anisotropic X-Y and Heisenberg ferromagnets. In particular, a comparison is estab- lished between some correlation functions of the X-Yand Heisenberg models.     

Study of critical properties of the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction.     

Quantum phase transition of the randomly diluted heisenberg antiferromagnet on a square lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.     

Computation of the effective potential for the two-dimensionalO(N) nonlinear σ-models

A Monte Carlo method for the computation of effective Hamiltonians for theO(N) nonlinear lattice σ-models is described. The procedure is based on simulations of auxiliary statistical mechanical systems with fixed block spins and thus avoids the simulation of systems with large correlation length. The method is applied to study the renormalization group flow of the effective potential for the Ising model, the XY model, and the Heisenberg ferromagnet in two dimensions. Some of the results are compared with second order high temperature expansions. For small block size a very good agreement is found in a large range of the inverse temperature β.     

Kinematical problem in Spin-wave theory

A spin-1/2, nearest neighbor Heisenberg Hamiltonian acting on a periodic,d-dimensional lattice is considered. Multi-spin-wave solutions to the Schrödinger equation for a Heisenberg ferromagnet involve an unlimited superposition of spin-reversal operators at sites. This violates the physical restriction that no more than one excitation reside on any one site. This exclusion rule affects spin-wave interaction—the determination of these effects is called the kinematical problem. A general nonperturbative treatment that includes kinematical effects in spin-wave theory is developed along the following lines. Using the property of the Heisenberg Hamiltonian that it does not couple states obeying the single occupation condition at all sites with states that violate the single-occupancy condition at some sites, the unphysical multiply occupied states can be eliminated by a nonunitary transformation of the eigenvalue equation. An overcomplete Hamiltonian matrix is obtained that contains all the physical eigenvalues as a subset of its spectrum. Overcompleteness is shown to be a large part of the kinematical problem and several schemes to handle it are discussed. The remainder of the kinematical problem lies in the nonorthogonality of spin waves. It is shown that a new type of distribution, one that is neither Bose nor Fermi, correctly describes free spin-wave statistics at all temperatures. This formal but nonetheless complete solution to the overcompleteness aspect of the kinematical problem is then carried over,in toto, to the boson formulation of the spin Hamiltonian. Application to the calculation of the partition function and to thermal Green's functions is noted.     

Twisted Heisenberg Doubles

We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg double and deduce the effect on the algebra of shifting the product and coproduct of the original twisted Hopf algebra. We conclude by showing that the quantum Weyl algebra, quantum Heisenberg algebras, and lattice Heisenberg algebras are all examples of the general construction.