Representation Of Spin Operators Research Articles

Higher-order solitons in an anisotropic Heisenberg spin chain

An anisotropic Heisenberg ferromagnetic spin chain model is studied by using Holstain-Primakoff representation. In the semiclassical limit, the exact solutions for bright and dark solitons are found by using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. These results show that the solutions can be expressed in terms of the elliptic integrals in different parameter regions. Some solutions for dark solitons are the innovation points in this paper.

Majorana spin liquid and dimensional reduction in Cs2CuCl4

The low-temperature behavior of the magnetic insulator Cs${}_{2}$CuCl${}_{4}$ can be modeled by an anisotropic triangular lattice spin-$1/2$ Heisenberg antiferromagnet with two different exchange couplings $J$ and ${J}^{\ensuremath{'}}\ensuremath{\approx}J/3$. We show that in a wide range of magnetic fields the experimentally observed field dependence of the crossover temperature ${T}_{c}$ for spin-liquid behavior can be explained within a mean-field theory based on the representation of spin operators in terms of Majorana fermions. We also show that for small magnetic fields the specific heat and the spin susceptibility both exhibit a maximum as a function of temperature at ${T}_{c}=J/2$. In the spin-liquid regime, the Majorana fermions can only propagate along the direction of the strongest bond, in agreement with the dimensional reduction scenario advanced by Balents [Nature (London) 464, 199 (2010)].

INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY

Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

Modeling the Elementary Excitations in an Alternating Cubic Ferrimagnetic Multilayer

A theoretical analysis of elementary excitations in the form of soliton modes in the alternating cubic spinel ferromagnetic multilayer is presented, using the coherent-state method coupled with the Holstein–Primakoff (HP) representation of spin operators. The Hamiltonian and the equations of motion for a cubic spinel ferromagnetic multilayer are rewritten in dimensionless forms, and two partial differential equations with nonlinear coupling are obtained. By the method of multiple scales, the equations are reduced to a nonlinear Schrodinger equation. Criteria for the existence of bright and dark solitons are studied. It is shown that due to the long-range and static dipole–dipole interactions, there exist different types of magnetic solitary excitations.

SD-CAS: Spin Dynamics by Computer Algebra System

A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples.

Stability of homogeneous magnetic phases in a generalizedt−Jmodel

We study the stability of homogeneous magnetic phases in a generalized $t\ensuremath{-}J$ model including a same-sublattice hopping ${t}^{\ensuremath{'}}$ and nearest-neighbor repulsion V by means of the slave-fermion--Schwinger-boson representation of spin operators. At mean-field order we find, in agreement with other authors, that the inclusion of further-neighbor hopping and Coulomb repulsion makes the compressibility positive, thereby stabilizing at this level the spiral and N\'eel orders against phase separation. However, the consideration of Gaussian fluctuation of order parameters around these mean-field solutions produces unstable modes in the dynamical matrix for all relevant parameter values, leaving only reduced stability regions for the N\'eel phase. We have computed the one-loop corrections to the energy in these regions, and have also briefly considered the effects of the correlated hopping term that is obtained in the reduction from the Hubbard to the $t\ensuremath{-}J$ model.

Effective action for the Kondo lattice model. New approach for S=1/2

In the partition function of the Kondo lattice (KL), spin matrices are exactly replaced by bilinear combinations of Fermi operators with the purely imaginary chemical potential λ=−iπ T/2 (Popov representation). This new representation of spin operators allows one to introduce new Green's Functions (GF) with Matsubara frequencies ω n=2 πT(n+ 1 4 ) for S= 1 2 . A simple temperature diagram technique is constructed with the path integral method. This technique is standard and does not contain the complicated combinatoric rules characteristic of most of the known variants of the diagram techniques for spin systems. The effective action for the almost antiferromagnetic KL problem is derived.

Self-Consistent Spin-Wave Approach to the Quantum Antiferromagnet on a Triangular Lattice

The self-consistent spin-wave approach proposed in the previous paper is applied to the XY and Heisenberg antiferromagnets with S =1/2 on a triangular lattice. Our approach is composed of two procedures. One is that the approximate boson representation of spin operators is derived from the equations of motion linearized about the equilibrium state on the assumption of the appearance of a long-range order (LRO). The other is that the following constraint is retained in the average: ( S j y ) 2 +( S j z ) 2 =1/2 when the x -axis is taken as the quantized one. Our estimates for the LRO and ground-state energy are in fairly good agreement with the results obtained by various methods. In contrast with the ordinary spin-wave theories, it is emphasized that the constraint becomes more effective in the systems with large spin fluctuations due to the zero-point motion.

Two Bose fluid picture of a Heisenberg ferromagnet

Using the Schwinger coupled boson representation of spin operators, we have derived a two Bose fluid like picture of a Heisenberg ferromagnet. In the magnetised state belowTc one of these fluids can be regarded as composed of magnons, the latter being excitations of the second condensed Bose fluid. Employing the coherent states technique for Schwinger bosons we have formulated ac-number description of the Heisenberg model. In contrast to previous proposals our description does not involve many body interactions and the Liouville operator is a second order differential operator.

On a representation for spin operators and its use in the theory of magnetism

On a representation for spin operators and its use in the theory of magnetism

On coherent spin states

Some properties of so called coherent spin states, analogous to the coherent states of the harmonic oscillator, are discussed. Polynomials of order 2S play an important role. The representation of spin operators in the space of coherent spin states is found. This representation is used to study the rotation operator.

Correct Evaluation of Some Thermodynamical Functions Using the Exact Boson Representation of Spin Operators

Correct Evaluation of Some Thermodynamical Functions Using the Exact Boson Representation of Spin Operators

Linked cluster theorem for the Abrikosov pseudo-fermion representation of spin operators

Abstract A linked cluster theorem is demonstrated for the self-energy of the average Green function of one electron moving in a low concentration of randomly positioned spins. The self-energy differs from what has previously been assumed by a frequency-independent but temperature-dependent factor.

The Quasi‐Pauli Representation of Spin Operators

AbstractA quasi‐Pauli representation of the spin operators is given. Since there are exact methods of representing the quasi‐Pauli operators by either Bose or Fermi operators, this enables an analysis of the processes in ferromagnets and antiferromagnets to be performed in a more completed way.

Theory of electron-electron interaction and superconductivity in dilute magnetic alloys above the Kondo temperature

The effective electron-electron interaction resulting from the virtual polarization of the impurity spin is investigated. Abrikosov's pseudofermion representation of spin operators has been applied. It is pointed out that the effective electron-electron interaction consists of two parts: 1) elastic scattering; 2) inelastic scattering. The second part shows a singularity of new type as (ω-ω′)−1, whereω-ω′ is the energy transfer between the two electrons. Both parts have been calculated in logarithmic approximation. Inspite of the fact that the second one is found to be lower by one order of the typical logarithmic Kondo terms than the first one, both terms can be of the same order of magnitude. Studying the superconducting transition temperature Abrikosov and Gor'kov's calculation is extended to include these interactions in any order of perturbation theory keeping the leading logarithmic terms. Our results are restricted to the temperature region well above the Kondo temperature. Considering the decrease of the superconducting transition temperature due to the magnetic impurities in the antiferromagnetic case the effect of the elastic scattering can be essentially reduced by the inelastic one.

Wick's Theorem for Spin Operators and Its Relation to the Coupled-Fermion Representation

It is shown that Wick's theorem and the linked diagram expansion theorem for S = ½ operators (applied elsewhere by the authors to discuss antiferromagnetic spin waves) can be derived by a direct application of conventional theorems to the coupled-fermion representation of spin operators.