When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamiltonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson operators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth-order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamiltonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson operators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth-order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.

Progress of Theoretical PhysicsSep 1, 19981 citation

Application of the Dyson-type boson mapping for low-lying electron excited states in molecules

Sadao Ohkido, Masahide Takahashi

In many-electron systems, particularly when it is the case that the system consists of quasi-particles having almost no interaction with each other, the approaches to considering a quasi-particle to be a basic particle are important. We propose a bosonization method of the system in which a quasi-particle consists of electron–hole pairs. Low-lying electron excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi-particles consists of the electron–hole pairs. We consider the fundamental model Hamiltonian, and transform this into the quasi-particle representation Hamiltonian. Then, we transform these quasi-particles into bosons by using the Dyson-type boson mapping method. The obtained Dyson-type boson Hamiltonian enables a straightforward interpretation of the low-lying electron excited states and facilitates their calculation. To confirm the usefulness of this method, we apply this to the | $\pi$ |-electrons system of the ethylene molecule.In many-electron systems, particularly when it is the case that the system consists of quasi-particles having almost no interaction with each other, the approaches to considering a quasi-particle to be a basic particle are important. We propose a bosonization method of the system in which a quasi-particle consists of electron–hole pairs. Low-lying electron excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi-particles consists of the electron–hole pairs. We consider the fundamental model Hamiltonian, and transform this into the quasi-particle representation Hamiltonian. Then, we transform these quasi-particles into bosons by using the Dyson-type boson mapping method. The obtained Dyson-type boson Hamiltonian enables a straightforward interpretation of the low-lying electron excited states and facilitates their calculation. To confirm the usefulness of this method, we apply this to the |$\pi$|-electrons system of the ethylene molecule.

Progress of Theoretical and Experimental PhysicsJun 1, 20150 citations

\pi

|-electrons system of the ethylene molecule.