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Physical review. B, Condensed matter

Ground state of a dissipative two-level system

Han Rongsheng, Gao Xianlong, Wang Kelin, Tong-Zhong Li

Published Dec 15, 2000• 4 citations
Publisher

Abstract

The ground state of a two-level system coupled to a dispersionless phonon bath is studied using the coherent approximation method. The ground-state energy and the tunneling reduction factor we obtain are in good agreement with the exact values in the whole parameter space. Since the real ground-state wave functions are well simulated, some other physical information about the system, such as the interaction energy and the interaction phonon numbers in each level and the whole system, are given. The interaction phonon numbers in the two-level system are found to increase with the coupling parameter s. In the intermediate coupling region, phenomenon of the population inversion and a maximum for the interaction phonon numbers versus ${\ensuremath{\delta}}_{0}/s$ have been found. Consisting with the exact results, our results show there is no evidence of the discontinuous localization-delocalization transition.

DOI
10.1103/physrevb.62.15579

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The ground state of a two-level system coupled to a dispersionless phonon bath is studied using the coherent approximation method. The ground-state energy and the tunneling reduction factor we obtain are in good agreement with the exact values in the whole parameter space. Since the real ground-state wave functions are well simulated, some other physical information about the system, such as the interaction energy and the interaction phonon numbers in each level and the whole system, are given. The interaction phonon numbers in the two-level system are found to increase with the coupling parameter s. In the intermediate coupling region, phenomenon of the population inversion and a maximum for the interaction phonon numbers versus \ensuremathδ0/s{\ensuremath{\delta}}_{0}/s\ensuremathδ0​/s have been found. Consisting with the exact results, our results show there is no evidence of the discontinuous localization-delocalization transition.
A new variational approach is proposed to study the ground-state of a two-level system coupled to a dispersionless phonon bath. By the extended coherent state, where the more phonon correlations are easily incorporated, we can obtain very accurate ground state energy and the tunnelling reduction factor in all regime of tunnelling matrix element d0 and coupling parameter s. The relative difference between the present ones and those by exact numerical diagonalization is less then 0.001%. In addition, some simple analytical results are given in the limits of δ 0 /s ↠ 0 and ∞.
We present some characteristic properties of the ground state of a two-level system linearly coupled to a phonon field. Such properties are valid over the whole range of the parameters appearing in the Hamiltonian of the system. The knowledge of these exact results provides a physical basis for an accurate variational determination of the ground state. A physical picture of the self-trapping transition is discussed in terms of particle-field correlations. Our treatment is based on operator methods combining symmetry considerations with some general properties of the lowest energy state.
The ground state of a two-level system coupled to a dispersionless phonon bath is studied using both a connected moments expansion and a truncated Lanczos tridiagonal scheme. We consider the spin-boson Hamiltonian, $\ifmmode \hat{H}\else \^{H}\fi{}=\ensuremath{-}{\ensuremath{\delta}}_{o}{\ensuremath{\sigma}}_{x}+{\ensuremath{\sum}}_{\mathbf{k}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathbf{k}}{a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{\mathbf{k}}+{\ensuremath{\sum}}_{\mathbf{k}}{g}_{\mathbf{k}}{(a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{+a}_{\mathbf{k}}){\ensuremath{\sigma}}_{z},$ where ${\ensuremath{\delta}}_{0}$ is the bare tunneling matrix element and gk{g}_{\mathbf{k}}gk​ represents the coupling to the k\mathbf{k}k phonon modes. Such systems have found relevance in applications to molecular polaron formation, exciton motion, and attenuation of sound in glasses. Our results are then compared to those of variational methods as well as an exact numerical diagonalization.
We present a systematic analysis of the ground state properties of a tunneling system coupled to an Ohmic bath. The nonadiabatic effects induced by coupling with tunneling particle, on the ground state properties of phonons are taken into account. For this we have considered both displacement and deformation of phonons via a variational treatment. The symmetry breaking transition, or the delocalization-localization transition, of the tunneling particle is presented and is compared with earlier known results. We also show that in the critical regime a gap will be opened near the zero momentum in the spectrum of the phonons. The modified phonon spectrum along with the phonon displacement field correlation functions have been calculated. It is shown that in the critical regime the tunneling system stabilizes the lattice against long wavelength fluctuations.