Holstein-Primakoff Boson Research Articles

Exactly solvable fermion-boson mapping representations

The Holstein-Primakoff boson mapping technique is applied to transform Hamiltonians defined in terms of the generators of the SU~2! and Sp~4! groups. These solvable models consist of a pair of fermions which interact with hard bosons. It is shown that the mapping to ideal bosons preserves the algebra and that exact matrix elements of the original fermionic Hamiltonian can be reconstructed from the bosonic representation. @S0556-2813~98!03006-4#

Modification of the Conventional Holstein-Primakoff Boson Representation for the su(1,1)-Algebra and Its Classical Counterpart

Modification of the Conventional Holstein-Primakoff Boson Representation for the su(1,1)-Algebra and Its Classical Counterpart

Quasi-Spin Squeezed State for Lipkin Model

To go beyond the usual Hartree·Fock approximation, a quasi-spin squeezed state is introduced in the Lipkin model. We define the quasi·spin squeezed state from the su(2)-coherent state in a manner similar to that for the ordinary boson squeezed state. In this paper, we deal only with the case that the parameters included in this state are time-independent. It is then seen that the exact energy eigenvalues of the ground state are reproduced with high accuracy in all regions of the force strength X by using the quasi-spin squeezed state. Also, it is shown that the quasi-spin squeezed state gives a classical counterpart with a certain correction for the Holstein-Primakoff boson representa· tion of su(2)·spin. We investigate uncertainty relations for su(2)-generators and the meaning of squeezing is clarified.

Three Forms of Boson Expansions for the su(2)-Spin System and Their c-Number Counterparts

In the framework of the Marumori-Yamamura-Tokunaga boson expansion, three forms for the su(2)-spin system are presented. The first is related with the well-known Holstein-Primakoff boson expansion and the second is the expansion reinvestigated in a previous paper by the present authors. The third is, in some sense, the original part of this paper. Corresponding with three forms, c-number counterparts are obtained by using three forms of wave packets defined in the su(2)-spin space. With the help of appropriate quantization rule, they go back to the original boson expansions. Furthermore, it is discussed if the c-number counterparts can be regarded as the classical counterparts. Finally, the relation to the su(1, 1)-algebraic model is discussed.

Some Remarks on the Binomial States

Using the Holstein–Primakoff boson realization of spin operators we can identify the binomial state with a particular spin coherent state. In so doing some properties of spin coherent states can be derived by simply using the binomial state. The displaced binomial state is introduced and its completeness relation is examined. That the concept of the binomial state can be extended to two-mode case is pointed out.

On the Hamiltonians Expressed in Terms of su(1, 1)-Generators for Describing Thermal Effects in Nuclear su(2)-Models

In order to develop a previously proposed method to investigate thermal effects in quantum many-particle systems, basic ideas are formulated in more general systems obeying su(2)-algebra. It is shown that Hamiltonians of a single orbit shell model with pairing correlation, the Lipkin model, a symmetric rigid rotor model and an asymmetric rigid rotor model have almost the same structure, that is algebraic structure of su(1, 1), by the use of the Holstein-Primakoff boson representation for su(2)-algebra and so-called phase-space doubling introduced to study thermal phenomena. It is also discussed that the interaction term between intrinsic system and external environment approximately represents the interesting physical process in each system at finite temperature.

Boson mapping of symplectic algebras with Abelian subalgebra mapped as coordinates

An extended Dyson and Holstein-Primakoff boson mapping is constructed for coordinate systems. Only functions which depend on even powers in the coordinates are considered. It is shown that the Holstein-Primakoff boson mapping for coordinate systems is different from the one using creation and annihilation operators, with some advantages in application. As an example the mapping is applied to the schematic model of constant gauge fields in Quantum-Chromo-Dynamics with SU(2) for color. Other possible applications related to field theory are briefly discussed.

Holstein–Primakoff Boson Realization for the Hydrogen Atom11The project supported by the Foundation of the Ph. D. Directing Programme of Chinese Universities.

We apply the Holstein–Primakoff transformation to the orbital angular momentum and the Runge–Lenz operators of a hydrogen atom to study its classical Kepler's problem. In this way the classical Kepler's frequency can be directly obtained without introducing Schwinger's boson realization and boson coherent states.

A Possible Classical Description for su(1, 1)-Spin Systems

With the aim of investigating dynamics of systems governed by su(1,1)- algebra, a possible state which can give us a classical counterpart for the su(1,1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent HartreeFock theory, the c-number analogue of the Holstein-Primakoff boson representation is obtained for the su(1,1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su(1,1)- spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced

Generalized Holstein-Primakoff images of fermion operators

The generalized Holstein-Primakoff (GHP) boson expansion is used to derive the images of single-fermion creation and annihilation operators in terms of collective bosons and ideal fermions for the case of well-deformed nuclei. The boson-fermion image of the quadrupole operator is then obtained, and is found to include a pure boson term, a pure fermion term, a boson-fermion exchange term and a further exchange term that mixes bosons with two quasifermions. We apply this method to a single- j model and show that in the deformed limit, the GHP expansion for the quadrupole operator gives a more appropriate description of quasiparticle energy systematics than does the corresponding operator obtained from a generalized seniority mapping. Finally, we consider the term that mixes bosons and quasifermion pairs within the context of the single- j model and show that it has precisely the form proposed phenomenologically in an extension of the IBM to high-spin states.

On the Boson Representations of SU(3) Algebra in the Basis SU(3) ⊃ U(1) + U(1)

The Dyson and Holstein–Primakoff boson realizations of the generators of SU(3) algebra have been given for the algebra chain SU(3) ⊃ U(1) + U(1), and a set of recursion formulae of the transformation matrix, which turn the Dyson onto the Holstein- Primakoff representation, have been presented. The multiplicity that can occur in the reduction of SU(3) ⊃ U(1) + U(1) is naturally determined.

Application of the Holstein-Primakoff boson expansion to two-phonon octupole states in 208Pb

Taking the coupling between the quadrupole and octupole interaction into account, the splitting of two-phonon octupole states in 208Pb and quadrupole moment Q(3-) are studied by using the generator coordinate method (GCM) and the Holstein-Primakoff boson expansion method (1940). The authors find that the energy splitting is small and depends more sensitively on the multipole force strength chi lambda ( lambda =2,3) than the quadrupole moment Q(3-).

Comment on "Skeleton boson realizations of collective subalgebras"

The skeleton boson realizations of fermion collective subalgebras proposed by Kim and Vincent are discussed. The Dyson boson mapping is found to play an essential role in the possibility of such realizations. A simple but instructive example is given to show that a straightforward application of the ``skeletonization procedure'' to the Holstein-Primakoff boson mapping may lead to serious errors in reproducing the fermion matrix elements. A possible way of constructing the modified skeleton Holstein-Primakoff realization of the collective subalgebra is suggested.

The classical limit for the Holstein-Primakoff representation in the soliton theory of Heisenberg chains

Soliton excitations in the anisotropic Heisenberg chain are studied in the classical limit by means of the Holstein-Primakoff boson representation, taking into account the complete series. The results obtained are equivalent to those obtained by the classical treatment of spins. The connection with different calculations using limited numbers of terms is established, as well as the relation to the generalised coherent-states method.

Approximate treatment of the Holstein-Primakoff-type boson mapping

The generalised Holstein-Primakoff boson representation of the bifermion operators is used to construct a boson image of the microscopic nuclear Hamiltonian. The microscopic analogue of the interacting boson model (IBM) Hamiltonian is obtained. It is shown how the square-root factor in the IBM Hamiltonian can be generalised so as to take into account its dependence on the angular momentum and seniority of the collective state. The method is applicable to systems where the assumption that the projection operator P is approximately equal to unity can be used. The method is proposed to include, apart from the collective quadrupole, other collective and non-collective degrees of freedom in the Hamiltonian.

Solitons in the anisotropic Heisenberg chain in the Holstein-Primakoff representation

It is shown that the Holstein-Primakoff boson representation of spin operators leads to the same soliton excitations, in the anisotropic Heisenberg chain, as the classical treatment of spins, if one retains the terms up to products of six Bose operators.

Coherent states for the harmonic series irreducible representations of U(p,q). I. Unitary operator coherent states

Unitary operator coherent states, as defined by Klauder (1963), Perelomov (1972) and Gilmore (1974), are considered for the harmonic series irreducible representations of U(p,q). Various properties of these states are reviewed, including their reproducing kernel and measure explicit forms, as well as the representation they lead to for the U(p,q) generators. Starting from a contraction of the su(p,q) Lie algebra, both Dyson and Holstein-Primakoff boson realisations of u(p,q) are obtained in terms of pq pairs of boson creation, annihilation operators and of the generators of a U(p)*U(q) intrinsic group. Such boson realisations are applied to determine the matrix elements of the U(p,q) generators between discrete bases classified according to the chain U(p,q) contains/implies U(p)*U(q). Finally, the isomorphism between so(4,2) and su(2,2) is employed to derive the corresponding properties of the SO(4,2) unitary operator coherent states for application in atomic physics.

Boson mapping of one-body operators in deformed nuclei

The generalized Holstein-Primakoff boson expansion is used to map one-body operators. A collective transformation is derived from the Hartree-Fock-Bogolyubov approximation in such a way as to preserve the density matrix. This prescription, when applied to a pairing + quadrupole model, yields almost complete s-d dominance.

Determination of the Sp(2d,R) generator matrix elements through a boson mapping

For the discrete series irreducible representations (( lambda +n/2)d) of Sp(2d,R), the determination of the Sp(2d,R) generator matrix elements in an Sp(2d,R) contains/implies U(d) basis is reduced to the much simpler calculation of boson operator matrix elements between U( nu ) contains/implies U(d) boson states, where nu =d(d+1)/2. The key of this reduction is the previously derived Holstein-Primakoff boson representation of the Sp(2d,R) generators. As an illustration, the case of Sp(6,R) is worked out in detail.

Approximate solutions of the particle-rotor model for decoupled bands

The particle-rotor model with a single nucleon in a configuration with large fixed $j$ is treated by means of the Holstein-Primakoff expansion. The small-oscillation approximation yields relatively simple analytic expressions for energies, alignments, electromagnetic moments, and transition rates of decoupled bands, which are surprisingly accurate over a broad range of $\frac{C}{A}$.NUCLEAR STRUCTURE Particle-rotor model; approximate analytic formulas; Holstein-Primakoff boson expansion.