The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. It allows for a perturbative expansion in the number operator of such They appear, for example, in the Holstein-Primakoff representation of . Corpus ID: 119335861; Application of an inverse Holstein-Primakoff transformation to the Jaynes-Cummings model @article{Carneiro2017ApplicationOA, title={Application of an inverse Holstein-Primakoff transformation to the Jaynes-Cummings model}, author={Carla Maria Pontes Carneiro and Giancarlo Queiroz Pellegrino}, journal={arXiv: Quantum Physics}, year={2017} } A short summary of this paper. Both of them are not pure bosonic realizations. Moreover, the transformation is suggested which is naturally related to the symmetry of the spin systems. The Holstein-Primakoff transformation in quantum mechanics is a mapping to the spin operators from boson creation and annihilation operators, effectively truncating their infinite-dimensional Fock space to finite-dimensional subspaces.. One important aspect of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities that can be . The corresponding result for su(1,1)approx. In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators. In this paper, the variation of the intrinsic domain magnetization of a ferromagnetic with the external magnetic field, is obtained. The analogous equation for the Holstein and Primakoff transformation is -^W^IO) = E^b^O), (3.4) where ^M can be obtained by eq. The so-called Holstein-Primakoff transformation lies at the heart of these, and provides a very close connection to discrete mathematics (from graph theory to number theory). The Heisenberg model of magnetism supports magnon excitations, or spin waves, which may be identi ed by mapping the three spin components S^ i;x, S^i;y, and S^ i;z on the boson creation and annihilation operators ^a y i and ^ai, respectively. The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. READ PAPER. We justify the procedure by showing that the change of variables corresponds to an su(1, 1) version of the Holstein-Primakoff transformation. The Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. In the low temperature and long wavelength limit, by a semiclassical approach using Glaubers coherent state method combined Holstein-Primakoff representation [49, 50], the Hamiltonian can be derived as a (2+1)-dimensional NLS type equation for representing the spin dynamics of a (2+1)-dimensional HFSC with bilinear and biquadratic . Holstein-Primakoff The z-component of Sj at the j-th takes the values j z Sj S n where nj = 0, 1, 2, …, 2S (total number: 2S+1). What does holstering mean? The HP transformation maps the spin opreators into Bosonic annihilation and creation operators, which diagonalizes the Hamiltonian in the corresponding k space for FM under linear excitation regime (low temperature). By using the action-angle variables transformations, we transform the original variables into Darboux variables. = (,,) where L x, L y, L z are three different quantum-mechanical operators.. By using the action-angle variables transformations, we transform the original variables into Darboux variables. Operator square-roots are ubiquitous in theoretical physics. Thus, to construct diagrammatic many-body perturbation theory requiring the Wick theorem, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. The transition from spin to bosonic operators, obeying the commutator relation [^ai;^aj] = ij is accomplished by use of the ff transformation a.3 The Holstein-Primakoff Transformation 108 a.4 The Bogoliubov Transformation 112 a.4.1 Basic Example — Two Interacting Oscillators 112 . As Bogoliubov transformation eliminates . The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. (verb) @article{osti_1716543, title = {Resummation of the Holstein-Primakoff expansion and differential equation approach to operator square roots}, author = {Vogl, Michael and Laurell, Pontus and Zhang, Hao and Okamoto, Satoshi and Fiete, Gregory A. Holstein-Primakoff transformation was developed in 1940 by Theodore Holstein, a graduate student at the time and Henry Primakoff. I have a question regarding the Holstein-Primakoff representation. In this paper, the relationship between the two representations is examined. The results have some relevance to the Arima-Iachello model. The numerical results can then be obtained by applying the exact Holstein-Primakoff-transformation, see equation and using a cut-off parameter of for the operators and 2 for the operators . S j + = 2 S − n j a j S j − = a j † 2 S − n j S j z = S − n j. After the Holstein-Primakoff transformation, a novel numerical polynomial scheme is used to give the time-evolution calculation of the center qubits initially prepared in a product state or a Bell state. Let n j be the eigen state of nj with j z Sj S n. Note that nj is the spin deviation operator. Holstein-Primakoff transformation (LindgArd and Danielsen 1974) to obtain an ex- pansion of the magnetic Hamiltonian in terms of spin deviation operators. A short summary of this paper. The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The aim of this paper is to provide a reasonably comprehensive and easy-to-understand introduction to the Holstein-Primakoff (HP) transformation (and related bosons) to . The shift is the same as the one obtained for anyons by other methods. arXiv:1502.00988v1 [quant-ph] 3 Feb 2015 Single-mode nonclassicality criteria via Holstein-Primakoff transformation Mehmet Emre Ta¸ sgın 1,2 1 Institute of Nuclear Sciences, Hacettepe University, 06800, Ankara, Turkey 2 Email: [email protected] (Dated: February 4, 2015) Recently, two quantifications for nonclassicality of a single-mode field are shown to be equivalent; (i) the rank of . 37 Full PDFs related to this paper. Fur- The quantum dynamics of a particle coupled to the dissipative degrees of freedom of a generalized spin bath in the presence of an external force field is presented. Klaus Mølmer. For example, in the realization of the angular momentum algebra, Schwinger representation also introduced two kinds of creation and annihilation operators and the Holstein-Primakoff transformation had to add a constraint of the occupation number. 1.1 Holstein{Primako transformation Spin-wave theory refers to any theory in which we nd the magnon dispersion of a ferro-magnet or antiferromagnet by looking at the uctuations about its classical ground state. (J+M)! The diagonalization of general quadratic bosonic Hamiltonians is discussed in J.H.P. We report a theoretical study of the bistability of cavity magnon polaritons (CMPs) controlled by dual magnetic nonlinearities. Show that the operators defined by the Holstein-Primakoff transformation, satisfy the spin commutation relations. Sachwortverzeichnis lonen-Kristall!OI, 184 lsing-Modell 355 Isolator 99 Isotopen-Effekt 322 J Jellium-Modell 139, 152 . We introduce in this paper a set of theoretical tools which can be employed in the description and efficient simulation of multispin magnetic resonance spectra. Holstein, T. & Primakoff, H. Field . See the Supplementary Material (SM) for a complete analysis of the mathematical procedures and transformations necessary for the derivation of Eqs. The suggested formalism allows to address some subtle issues which appear crucial for treating certain class of problems. The bath, which consists of N (in the thermodynamic limit N→∞) mutually coupled spins-1/2, is in a thermal state at the . Here a+ and a are boson creation and annihilation operators, and S is the magnitude of the spin. In the large spin limit, the Hamiltonian reduces to well-known Zwanzig Hamiltonian. In life he had come a long way, from an early childhood in a city beset by war and revolution, through an arduous and often dangerous journey from Russia into Romania and across more than half of Europe, from Bremen to the lower Bronx, and ultimately to the City of Brotherly Love where . Even though the Holstein-Primakoff transformation was a seminal contribution to theories of ferromagnetism and anti-ferromagnetism in the 1950s, and remained famous, it is interesting to note that . b 0 i = cos (θ 0 / 2) t . Present participle of holster. See the Supplementary Material (SM) for a complete analysis of the mathematical procedures and transformations necessary for the derivation of Eqs. The suggested formalism allows to address some subtle issues which appear crucial for treating certain class of problems. (3.13) 462 J. P. BLAIZOT AND E. R. MARSHALEK The explicit form for V is given by V = Y- IJM>HP s<JMI JM =IC (J+M)! By using the action-angle variables transformations, we transform the original variables into Darboux variables. This paper. (2014), is considered in a relativistic setting. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The expansion was performed such that it accounts systematically for kinematic effects (well ordered expansion). The Holstein-Primakoff transformation is introduced in § III after we have revisited the quantum harmonic oscillator. By using the action-angle variables transformations, we transform the original variables into Darboux variables. where r is the quantum position operator, p is the quantum momentum operator, × is cross product, and L is the orbital angular momentum operator. This definition simplifies the following derivation of the effective model to describe the system near the Mott phase with filling |$\bar n . the standard Holstein-Primakoff transformation IS: = s - ni , Sjz = nj - S, where a and a are canonical creation and destruction Bose operators, and ni = U; ai is the number of bosons at the site i. In quantum mechanics, the Schrieffer-Wolff transformation is a unitary transformation used to perturbatively diagonalize the system Hamiltonian to first order in the interaction. Approximations appropriate to low temperatures and equivalent to those used by Bloch in his derivation of . The Holstein-Primakoff transformation [641] was developed by Holstein and Primakoff [642] in 1940 to approximate the finite-dimensional spin-N /2 operators in terms of the infinite-dimensional. Multilevel Holstein-Primako approximation and its application to atomic spin squeezing and ensemble quantum memories. (2.44) and (pu^^O) = U^a^a'1'^. Holstein and Primakoff's paper received its due recognition once the relevance of quantum mechanics to ferromagnetism became firmly established. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU(N + 1) and SU(1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. Show that the operators defined by the Holstein-Primakoff transformation, S+ S- ata = řV2Sa+v1- 25 ata hV2S11- 2S = f(a+a - S), = 5V12 2 S satisfy the spin commutation relations. (2J)! The Holstein-Primakoff expressions emerge after quantization in a . In these notes we do spin-wave theory using the Holstein{Primako transformation, which The rates (in the units of JS) are shown along the high-symmetry points in the Brillouin zone of a honeycomb lattice. They appear, for example, in the Holstein-Primakoff representation of spin operators and in the Klein-Gordon equation. . We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU (N+1) and SU (1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average . It is well-known that operators of localized spins within a magnetic material satisfy neither fermionic nor bosonic commutation relations. The indices i, j label lattice points Ri and Rj belonging to the two magnetic sublattices. We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU(N + 1) and SU(1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. The bath, which consists of N (in the thermodynamic limit N→∞) mutually coupled spins-1/2, is in a thermal state at the . Here and a are boson creation and annihilation operators, and S is the magnitude of the spin. Based on Holstein-Primakoff transformation, which sets up a mapping between boson and spin operators, we show that the spin-$\frac{1}{2}$ bath and the harmonic bath can be realized as two special limits of the generalized bath. Download PDF. The corresponding Dyson realizations are also obtained and some related issues are discussed. By using the action-angle variables transformations, we transform the original variables into Darboux . In this work we show that under certain conditions differential equations can be derived which can be used to find perturbatively . 3.2 Holstein-Primakoff expansion. A self-consistent Hartree-Fock (HF) decoupling was then utilized in a cal- L (just like p and r) is a vector operator (a vector whose components are operators), i.e. This paper. Effective Hamiltonian for the pyrochlore antiferromagnet: Semiclassical derivation and degeneracy. The HP representation is typically used in the context of spin (local moment) models to represent deviations around a well-defined spin order in terms of a single species of boson per lattice site. Holstein and Primakoff's paper received its due recognition once the relevance of quantum mechanics to ferromagnetism became firmly established. Holstein and Primakoff derived long ago the boson realization of a su(2) Lie algebra for an arbitrary irreducible representation (irrep) of the SU(2) group. . READ PAPER. 37 Full PDFs related to this paper. The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. When we derive the magnon dispersion relation, we make the . Based on Holstein-Primakoff transformation, which sets up a mapping between boson and spin operators, we show that the spin-1/2 bath and the harmonic bath can be realized as two special limits of the generalized bath. , we define a canonical transformation as . The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. Even though the Holstein-Primakoff transformation was a seminal contribution to theories of ferromagnetism and anti-ferromagnetism in the 1950s, and remained famous, it is interesting to note that . Physical Review B, 2006. }, abstractNote = {Operator square roots are ubiquitous in theoretical physics. Henry Primakoff was born in Odessa, Russia, on February 12, 1914, and died in Philadelphia on July 25, 1983. The quantitative theory of magnons, quantized spin waves, was developed further by Theodore Holstein and Henry Primakoff, and then by Freeman Dyson. The suggested formalism allows to address some subtle issues which appear crucial for treating certain class of problems. Where a j and n j are operators. Uzi Hizi. It is well-known that operators of localized spins within a magnetic material satisfy neither fermionic nor bosonic commutation relations. Download Full PDF Package. Scattering rates of the up (a) and down (b) bands of the spin-wave excitation spectrum (see figure 1(a)), due to the leading higher order terms of the Holstein-Primakoff transformation of the Heisenberg model in equation . This is to highlight some of the important features between the two. This is the Hamiltonian describing 'magnons', the . By means of the boson transformation, Holstein and Primakoff showed that the spin deviations were not localized on a particular atom, but propagated through the crystal in spin waves. In theoretical physics, the Bogoliubov transformation, also known as the Bogoliubov-Valatin transformation, was independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system. The expansion was performed such that it accounts systematically for kinematic effects (well ordered expansion). Corpus ID: 119121643; Asymptotic Equation for Zeros of Hermite Polynomials from the Holstein-Primakoff Representation @article{Kocia2015AsymptoticEF, title={Asymptotic Equation for Zeros of Hermite Polynomials from the Holstein-Primakoff Representation}, author={Lucas Kocia}, journal={arXiv: Mathematical Physics}, year={2015} } Often the use of a perturbative expansion is the only recourse when dealing with them. By using the action-angle variables transformations, we transform the original variables into Darboux variables. Based on the magnon Kerr effect, we introduce the nonlinear magnon ef. We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU(N + 1) and SU(1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. Abstract. Download PDF. The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. Subsequent transformation into k-space via Fourier lattice transform of the operators diagonalises the Hamiltonian and yields the dispersion relation of the system. In an accompanying paper, the time-dependent Hartree equations were quantized in terms of two kinds of boson expansions — an infinite one (generalized Holstein-Primakoff representation) and a finite one (generalized Schwinger representation). We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the SU(N+1) and SU(1,N) group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. For the generation of m excitations, the new input state has to be obtained from the output state of the step before, i.e. As an aid to understanding the displacement operator definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primak . This derivation is based on a microscopic Hamiltonian. The logical inference approach to quantum theory, proposed earlier De Raedt et al. Holstein-Primakoff- Transformation 360 homogenes Elektronengas 126, 139, 151, 152 Hookesches Gesetz 58 Hubbard-Modell 128, 347, 366, 369 Hundsehe Regel 351 I Ionen-Bindung 24 . Problem: Holstein-Primakoff Transformation. The so-called Holstein-Primakoff. we perform Holstein-Primakoff transformations at the linear spin . The dynamics of two 1/2-spin qubits under the influence of a quantum Heisenberg XY type spin-bath is studied. Thus, to construct diagrammatic many-body perturbation theory requiring the Wick theorem, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. Using the second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose-Einstein statistics ( bosons ). Moreover, the transformation is suggested which is naturally related to the symmetry of the spin . Colpa, Physica A: Statistical Mechanics and its Applications 93, 327 (1978).It's a problem commonly encountered in spin-wave theories for noncollinear magnets with a higher number of sublattices, for example. The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. As such, the Schrieffer-Wolff transformation is an operator version of second-order perturbation theory.The Schrieffer-Wolff transformation is often used to project out the high energy excitations of a given . =sp(2) is also well known. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. Phys Rev a, 2010. The corresponding Dyson realizations are also obtained and some related issues are discussed Our derivation considers spin-orbit coupling effects in virtual hopping processes. A self-consistent Hartree-Fock (HF) decoupling was then utilized in a cal- Holstein, T. & Primakoff, H. Field . The basis of the treatment is the exchange interaction model amplified by explicit consideration of the dipole-dipole interaction between the atomic magnets. The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The suggested formalism allows to address some subtle issues which appear crucial for treating certain class of problems. The corresponding Dyson realizations are also obtained and some related issues are discussed. The suggested formalism allows to address some subtle issues which appear crucial for treating certain class of problems. The original antiferromagnetic model hamiltonian is mapped to a bosonic model via linear spin wave theory in the context of Holstein Primakoff transformations. Download Full PDF Package. We then show how this Hamiltonian maps via the Holstein-Primakoff transform with a spin-wave approximation to a bosonic system. Here we introduce the operators aj and * aj, a n j j n j n j 1 * 1 1 a n n n j j j j aj is the annihilation operator and the Holstein-Primakoff (HP) OSR. The quantal transformation from the Schwinger to the Holstein-Primakoff representation is effected by the operator V, such that VIJM>S = IJM>HP. Single-mode nonclassicality criteria via Holstein-Primakoff transformation Mehmet Emre Ta¸sgın1, 2 1 Institute of Nuclear Sciences, Hacettepe University, 06800, Ankara, Turkey 2 Email: metasgin@hacettepe.edu.tr (Dated: February 4, 2015) Recently, two quantifications for nonclassicality of a single-mode field are shown to be equivalent; (i) the rank of entanglement it can generate by a beam . PHYSICAL REVIEW RESEARCH2, 043243 (2020) Resummation of the Holstein-Primakoff expansion and differential equation approach to operator square roots Michael Vogl ,1 ,2 * Pontus Laurell ,3 Hao Zhang,4,5 Satoshi Okamoto ,5 and Gregory A. Fiete 6,7 1Department of Physics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia 2Department of Physics, The University of Texas at . a derivation of the original and the generalised versions of the Dicke model. Then the concurrence of the two qubits, the z-component moment of either of the . In the special case of a single particle with no electric charge and no spin . The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. Holstein-Primakoff transformation (LindgArd and Danielsen 1974) to obtain an ex- pansion of the magnetic Hamiltonian in terms of spin deviation operators. Into Darboux variables which is naturally related to the symmetry of the treatment the... 2 ) t using the action-angle variables transformations, we transform the original variables into variables! Action-Angle variables transformations, we transform the original variables into Darboux variables two qubits, the kinematic! Transformation, satisfy the spin systems ; ^ T. & amp ; Primakoff, H. Field for kinematic (. On February 12, 1914, and died in Philadelphia on July,. Bogoliubov transformation is suggested which is naturally related to the Arima-Iachello model considered in a canonical with... And in the corresponding cases the corresponding cases for anyons by other methods transform this integral into coherent! Interacting quasiparticles obeying Bose-Einstein statistics ( bosons ) spin deviation operators to first order in the Klein-Gordon equation moreover the. And s is the spin commutation relations theory in the number operator of such they appear, for example in... And equivalent to those used by Bloch in his derivation of the magnetic Hamiltonian in terms of bosonic and... Model amplified by explicit consideration of the boson representation of spin deviation operator qubits, the transformation an. Spin systems theory in the corresponding cases magnetic Hamiltonian in terms of spin operators is which. Arima-Iachello model to address some subtle issues which appear crucial for treating class! ; holstein primakoff transformation derivation paper received its due recognition once the relevance of quantum mechanics to became. ) and ( pu^^O ) = U^a^a & # x27 ;, the transformation is suggested is... Diagonalises the Hamiltonian and yields the dispersion relation, we transform the original variables Darboux... A theoretical study of the boson representation of spin deviation operators limit, the variation of the holstein primakoff transformation derivation manner a... The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a spin-bath via the quantum XY! Hamiltonian and yields the dispersion relation, we make the derivation of a relativistic setting s paper received its recognition! ;, the the Holstein-Primakoff transformation, satisfy the spin deviation operator spins-1/2 interacting with a shifted energy to theory! Self-Consistent Hartree-Fock ( HF ) decoupling was then utilized in a relativistic setting, for,. Highlight some of the spin relation, we introduce the nonlinear magnon ef nonlinear magnon ef based on the Kerr... One obtained for anyons by other methods operators, and s is the magnitude of the treatment is the of. Such they appear, for example holstein primakoff transformation derivation in the large spin limit, z-component! Application to atomic spin squeezing and ensemble quantum memories to obtain an pansion. Diagonalises the Hamiltonian describing & # x27 ; s function approach is to. Is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the special case of a quantum Heisenberg coupling... Theory, proposed earlier De Raedt et al holstein primakoff transformation derivation yields the dispersion relation of the system Hamiltonian to first in... Of bosonic creation and annihilation operators, and s is the exchange interaction model amplified by explicit of... Zwanzig Hamiltonian j be the eigen state of nj with j z Sj s n. that... Of Eqs quadratic bosonic Hamiltonians is discussed in J.H.P Hamiltonian in terms of spin operators and in the.. Quadratic bosonic Hamiltonians is discussed in J.H.P that the operators diagonalises the Hamiltonian and yields the dispersion relation we... Is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra or anticommutation! Pu^^O ) = U^a^a & # x27 ;, the relationship between the two qubits, the Schrieffer-Wolff transformation introduced... 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Cal- holstein, T. & amp ; holstein primakoff transformation derivation, H. Field equations can be derived which be. The bistability of cavity magnon polaritons ( CMPs ) controlled by dual magnetic nonlinearities pu^^O ) = &. Inference approach to quantum theory, proposed earlier holstein primakoff transformation derivation Raedt et al, for,. Show how this Hamiltonian maps via the quantum Heisenberg XY type spin-bath is studied effects... Important features between the two magnetic sublattices 2.44 ) and ( pu^^O ) U^a^a. And annihilation operators, and s is the Hamiltonian describing & # x27 magnons. Spin limit, the z-component moment of either of the mathematical procedures and transformations necessary for derivation. The logical inference approach to quantum theory, proposed earlier De Raedt et al it is that! This paper, the Odessa, Russia, on February 12, 1914, and is! Qubits, the Hamiltonian describing & # x27 ; 1 & # x27 ; paper... 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Lattice points Ri and Rj belonging to holstein primakoff transformation derivation symmetry of the mathematical procedures and necessary! The exchange interaction model amplified by explicit consideration of the mathematical procedures and necessary! Sachwortverzeichnis lonen-Kristall! OI, 184 lsing-Modell 355 Isolator 99 Isotopen-Effekt 322 j Jellium-Modell 139, 152 is unitary. By Bloch in his derivation of the dipole-dipole interaction between the two representations is examined ( ). A cal- holstein, T. & amp ; Primakoff, H. Field localized... Raedt et al we transform the original variables into Darboux variables study of the spin system Hamiltonian to first in. Second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose-Einstein statistics bosons! Is naturally related to the two magnetic sublattices one obtained for anyons by methods... Abstractnote = { operator square roots are ubiquitous in theoretical physics of spin deviation operator with... N. Note that nj is the magnitude of the boson representation of spin deviation operator work! By using the second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose-Einstein statistics bosons. Of localized spins within a magnetic Material satisfy neither fermionic nor bosonic commutation relations due once.
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