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Solid State Communications

Tunneling coherence and localization in a spin-boson system: A dynamic extension of the Anderson orthogonality theorem

Toshio Tsuzuki

Published Sep 1, 1989• 4 citations
Publisher
DOI
10.1016/0038-1098(89)90203-2

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Progress of Theoretical Physics•Nov 1, 1982•55 citations
We present a dynamic theory of the ground state of a spin boson system. We show the infrared divergence due to the zero-point fluctuation of displaced bosons is completely compensated by that due to the dynamical fluctuation of coherently excited bosons for arbitrary positive power sof the frequency dependence of the spectral density of interaction. We propose this as the theorem of dynamic compensation of the infrared divergence. In this sense our theory is a dynamic extension of the Anderson orthogonality theorem. Solving the eigenvalue equation in the lowest approximation we find that (1) there exists a critical value αc of the interaction strenght below which the ground state (GS) is the tunneling state for arbitrary positive s, (2) for s>1/2 the GS is the localized state above αc but (3) for 1/2>s>0 we find the localized GS above another critical value α'c>αc and we have found nothing definite, for the moment, for αc≪α≪α'c and (4) the tunneling gap tends to zero continuously when α approaches αc.
By using a variation method we study the ground state of a tunneling particle coupled to many bosons in a double-well potential. The boson system is assumed to have dense low-energy excitations, just as taken by Chakravarty and Leggett to discuss the dissipative effect in macroscopic quantum phenomena. We examine reduction of the tunneling matrix and eventual localization of the particle due to boson excitations for arbitrary strengths of tunneling and coupling parameters. Ground state energy is evaluatied. Continuous as well as discontinuous changes from tunneling to localized states are found when the coupling parameter increases. The results are related to the orthogonality of many-particle ground states, as known for many-electron system as Anderson's theorem.
Journal of the Physical Society of Japan 65 (1996) pp. 2910–2916 An Estimate of the Asymmetry of Ag 3d XPS Lines Takashi Ikeda Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 73–84 Application of the Orthogonality Theorem to the Motion of a Charged Particle in Metals Kosaku Yamada, Akio Sakurai and Motomu Takeshige Progress of Theoretical Physics Vol. 72 No. 2 (1984) pp. 195–201 Diffusion of Positive Muon and Orthogonality Theorem Kosaku Yamada Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1342–1351 A Closed Form Solution for the Hopping Rate of Charged Particles in Metals Kosaku Yamada, Akio Sakurai and Sasuke Miyazima Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1030–1043 Application of the Orthogonality Theorem to the Motion of a Charged Particle in Metals. II Kosaku Yamada, Akio Sakurai, Sasuke Miyazima and Hae Sun Hwang Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1048–1057 New Formalism for an Overlap Integral of the Anderson Orthogonality Theorem Akihide Oguchi and Kei Yosida Progress of Theoretical Physics Vol. 76 No. 5 (1986) pp. 999–1007 Ground State of a Tunneling Particle Coupled to Boson Excitaions in a Double-Well Potential Akiko Tanaka and Akio Sakurai Progress of Theoretical Physics Vol. 78 No. 3 (1987) pp. 583–590 Anderson Orthogonality Theorem Takeshi Kitamura, Akihide Oguchi and Kei Yosida Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 917–929 Ground State of a Spin-Boson System Toshio Tsuzuki Progress of Theoretical Physics Vol. 90 No. 1 (1993) pp. 43–51 Overlap Integral between the Ground States of an Electron Gas Corresponding to Two Positions of a Scattering Potential K. Vladár Progress of Theoretical Physics Supplement No.106 (1991) pp. 147–156 Orthogonality Exponents in Low-Dimensional Metals K. Schönhammer